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Paper Citation Record · LEDGER

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation

As of 21 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 0 inbound Pith citation observations for arXiv:2412.17117.

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pith.paper-citation-record.v1
2412.17117 v2

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measured 55 of 55 reference resolution

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measured 55 of 55 standing notices

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

55 of 55 outbound references displayed

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Outbound references

Observation 472e4f08-d163-4240-be6a-91f50c87f250 · outbound

This paper cites Petviashvili type methods for traveling wave computations: I.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Petviashvili type methods for traveling wave computations: I

Reference 1

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Observation 424bc6ad-e961-4ad9-89e2-679303a8380a · outbound

This paper cites Dispersive nonlinear shallow-water equations.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Dispersive nonlinear shallow-water equations

Reference 2

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Observation 07715dc6-9a4e-4532-8c21-80c00626de9f · outbound

This paper cites A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies

Reference 3

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Observation 897cdd87-2949-4083-9984-fd8403bb8245 · outbound

This paper cites Perfectly matched layers methods for mixed hyperbolic–dispersive equations.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Perfectly matched layers methods for mixed hyperbolic–dispersive equations

Reference 4

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Observation 689514c2-34a2-45ff-85f0-3af31948fa04 · outbound

This paper cites Julia: A fresh approach to numerical computing.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Julia: A fresh approach to numerical computing

Reference 5

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Observation 7215c4c3-c6d3-4925-a041-c3603cfafc40 · outbound

This paper cites Accurate Solution of the Nonlinear Schr\"{o}dinger Equation via Conservative Multiple-Relaxation ImEx Methods.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Accurate Solution of the Nonlinear Schr\"{o}dinger Equation via Conservative Multiple-Relaxation ImEx Methods

Reference 6

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Observation 67813d07-b0ea-4b46-8816-a258285750cb · outbound

This paper cites Multiple-relaxation Runge Kutta methods for conservative dynamical systems.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Multiple-relaxation Runge Kutta methods for conservative dynamical systems

Reference 7

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Observation 6c24290e-af59-4b87-8ade-04996e1cd194 · outbound

This paper cites Ketcheson, Hendrik Ranocha, and Jochen Sch¨ utz.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Ketcheson, Hendrik Ranocha, and Jochen Sch¨ utz

Reference 8

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 9a8dd531-d8d0-4ed8-8295-032ed68c8cd7 · outbound

This paper cites Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review

Reference 9

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Observation ca509468-8ba6-4767-a199-39997e8f1a95 · outbound

This paper cites Convective wave breaking in the KdV equation.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Convective wave breaking in the KdV equation

Reference 10

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Observation 3bb954c2-4ec9-4d11-a717-202ac7021bc3 · outbound

This paper cites Camassa, D.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Camassa, D

Reference 11

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Observation 7b3caba2-4930-44a8-ad23-2425ba0c22f9 · outbound

This paper cites Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid

Reference 12

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Observation d937f1af-1b3e-474e-8f7c-a9fc8e958c78 · outbound

This paper cites Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Hyperbolic model for free surface shallow water flows with effects of dispersion, vorticity and topography

Reference 13

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Observation e2c90c4b-006d-44aa-ae8d-4c81cb7c811c · outbound

This paper cites Finite propagation speed for the Camassa–Holm equation.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Finite propagation speed for the Camassa–Holm equation

Reference 14

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Observation fb19a3cc-63e2-40f1-8c44-6e08cbd22432 · outbound

This paper cites The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations

Reference 15

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Observation f2c2be1f-7622-43b1-8806-ae7103087ed1 · outbound

This paper cites Makie.jl: Flexible high-performance data visualization for Julia.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Makie.jl: Flexible high-performance data visualization for Julia

Reference 16

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Observation 4971bed7-3690-4d6a-93c3-cbc9cfd62c3c · outbound

This paper cites Accuracy and conservation properties in numerical in- tegration: the case of the Korteweg-de Vries equation.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Accuracy and conservation properties in numerical in- tegration: the case of the Korteweg-de Vries equation

Reference 17

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 6df7ebf3-2690-431d-9a80-0458fa5554a9 · outbound

This paper cites A first order hyperbolic reformulation of the Navier-Stokes- Korteweg system based on the GPR model and an augmented Lagrangian approach.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation A first order hyperbolic reformulation of the Navier-Stokes- Korteweg system based on the GPR model and an augmented Lagrangian approach

Reference 18

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Observation 6e4e320f-6a61-449f-8f04-ccf0f09002e5 · outbound

This paper cites Extended Lagrangian approach for the defocusing nonlinear Schr¨ odinger equation.Studies in Applied Mathematics , 142(3):336–358, 2019.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Extended Lagrangian approach for the defocusing nonlinear Schr¨ odinger equation.Studies in Applied Mathematics , 142(3):336–358, 2019

Reference 19

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Observation 05c6492b-c5c3-43a2-8325-84d0f4ccc959 · outbound

This paper cites Hyperbolic relaxation models for thin films down an inclined plane.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Hyperbolic relaxation models for thin films down an inclined plane

Reference 20

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Observation 501492a0-66d8-45d2-bf2d-5340c0a37fd2 · outbound

This paper cites The numerical integration of relative equilibrium solu- tions.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation The numerical integration of relative equilibrium solu- tions

Reference 21

Resolution
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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation f60799f5-3b44-4b4a-92e1-89a1f0b3ebfb · outbound

This paper cites The numerical integration of relative equilibrium so- lutions.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation The numerical integration of relative equilibrium so- lutions

Reference 22

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Observation d9422939-e079-4609-aa0c-c07a67829065 · outbound

This paper cites An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes

Reference 23

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Source-reported events for the cited work

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Observation b0658314-aee6-414d-8432-dcc8de2e1ee2 · outbound

This paper cites A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves

Reference 24

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation ea386788-f622-4098-bf52-04c256c7a4d2 · outbound

This paper cites Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations

Reference 25

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Observation b6ca75db-6e95-4097-b0aa-26f29e16ede5 · outbound

This paper cites The design and implementation of FFTW3.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation The design and implementation of FFTW3

Reference 26

Resolution
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Source-reported events for the cited work

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Observation 4f7015d7-a2af-4dfc-ab80-3b301a13a73c · outbound

This paper cites The conduit equation: hyperbolic ap- proximation and generalized Riemann problem.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation The conduit equation: hyperbolic ap- proximation and generalized Riemann problem

Reference 27

Resolution
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Source-reported events for the cited work

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Observation 7c2b0f89-27cd-44db-9d7f-6eec322b2c55 · outbound

This paper cites Hyperbolic approximation of the BBM equation.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Hyperbolic approximation of the BBM equation

Reference 28

Resolution
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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation d6b4548d-7bac-480e-bffe-e11a14538149 · outbound

This paper cites Dispersive nonlinear shallow-water equations: some preliminary numerical results.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Dispersive nonlinear shallow-water equations: some preliminary numerical results

Reference 29

Resolution
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Observation ae005a15-cc0a-459c-8606-6f5a8f6b73ec · outbound

This paper cites Array programming with NumPy.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Array programming with NumPy

Reference 30

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Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Unresolved cited work

Reference 31

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Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Unresolved cited work

Reference 32

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 4b632693-97dc-4e75-bf75-ab2fac686cb7 · outbound

This paper cites Asymptotic-preserving schemes for multiscale physical problems.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Asymptotic-preserving schemes for multiscale physical problems

Reference 33

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source=pdf_text observed=2026-08-11T05:55:17.972943Z digest=sha256:18779fb1b6eccd61ce8e8846e818f1da5384d80b379af2a5e0d38a4a011c5c65

Observation a7052495-c43c-48b0-9dd0-93869a64aa22 · outbound

This paper cites Additive Runge–Kutta schemes for convection– diffusion–reaction equations.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Additive Runge–Kutta schemes for convection– diffusion–reaction equations

Reference 34

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Observation 2fa1cdfd-efb9-4081-8810-d612c9dbd888 · outbound

This paper cites Relaxation Runge–Kutta methods: Conservation and stability for inner-product norms.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Relaxation Runge–Kutta methods: Conservation and stability for inner-product norms

Reference 35

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Observation b01dc8f5-5a3e-4e11-ab82-eaa2ebd78fc3 · outbound

This paper cites Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation

Reference 36

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Observation 07d65282-a8a4-4252-89d9-8d58b579de96 · outbound

This paper cites Traveling wave solutions of the Degasperis–Procesi equation.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Traveling wave solutions of the Degasperis–Procesi equation

Reference 37

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source=pdf_text observed=2026-08-11T05:55:17.991733Z digest=sha256:7ef88fdf8302ea4ea62fe6497e862130f04e09813f7e9c39f2a007008b2d5861

Observation b2cd5fb0-e572-4fd7-b0ea-784fb36a2d1d · outbound

This paper cites Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs

Reference 38

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source=pdf_text observed=2026-08-11T05:55:17.996306Z digest=sha256:453545ac8a1ce3507346d6c2d9a58bc4cbc1538f2a5e8292241a2df75e33c1a6

Observation 5c932466-c959-4f3c-9bd2-1617e0efa284 · outbound

This paper cites A new formulation of hyperbolic Navier- Stokes solver based on finite volume method on arbitrary grids.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation A new formulation of hyperbolic Navier- Stokes solver based on finite volume method on arbitrary grids

Reference 39

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source=pdf_text observed=2026-08-11T05:55:18.000873Z digest=sha256:7a901f40e319e73a29664a73eb4bf1cb20cc0d5e890273e827ee8ad5ad486a5b

Observation cb1a78ae-9e61-451f-8004-651cefc7637b · outbound

This paper cites Diagonal-norm upwind SBP operators.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Diagonal-norm upwind SBP operators

Reference 40

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source=pdf_text observed=2026-08-11T05:55:18.005429Z digest=sha256:e1c8a1667f9e885aae3080d772ec6c6dd4706fb2e9eb973ed8087f0f19a1c384

Observation a3fa3205-3de9-4351-811a-64cec96a989d · outbound

This paper cites A first-order hyperbolic system approach for dispersion.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation A first-order hyperbolic system approach for dispersion

Reference 41

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source=pdf_text observed=2026-08-11T05:55:18.009644Z digest=sha256:073e362e9791a9a424eed32fccbb74fc3bbbddfd02a61103d2190b74cbfffa1a

Observation f3d4450c-2fce-4974-9895-4baa0bafc43e · outbound

This paper cites Implicit–explicit Runge–Kutta schemes and applications to hyperbolic systems with relaxation.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Implicit–explicit Runge–Kutta schemes and applications to hyperbolic systems with relaxation

Reference 42

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source=pdf_text observed=2026-08-11T05:55:18.014151Z digest=sha256:09451e69154c3c7f31a081fcf49d6119509d9864444edd306bea18d1420daad1

Observation 26e376d2-6891-4e26-9877-d09384c66169 · outbound

This paper cites Mimetic properties of difference operators: Product and chain rules as for func- tions of bounded variation and entropy stability of second derivatives.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Mimetic properties of difference operators: Product and chain rules as for func- tions of bounded variation and entropy stability of second derivatives

Reference 43

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source=pdf_text observed=2026-08-11T05:55:18.018556Z digest=sha256:a8c4273f861eb8643753e8355b0af30453c3e3dff11e48a900f8930b9d8b6632

Observation a3ed8d5b-f9c0-4c25-ba61-ca0ddc380ccd · outbound

This paper cites SummationByPartsOperators.jl: A Julia library of provably stable semidiscretiza- tion techniques with mimetic properties.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation SummationByPartsOperators.jl: A Julia library of provably stable semidiscretiza- tion techniques with mimetic properties

Reference 44

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source=pdf_text observed=2026-08-11T05:55:18.023387Z digest=sha256:94cefafd00f11652ef9e7231ed0ac898368cb575f8dca795c7a2d987d3d809ad

Observation 6e4a8256-6972-47d2-a483-6df3799269da · outbound

This paper cites General relaxation methods for initial-value problems with application to multistep schemes.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation General relaxation methods for initial-value problems with application to multistep schemes

Reference 45

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source=pdf_text observed=2026-08-11T05:55:18.027835Z digest=sha256:7eae503b364007be52977fb704527c1fc37f4fb659a2a1b2eff8b8c31c7036ab

Observation 0d4d38b7-2302-4d10-b058-0201243695df · outbound

This paper cites A broad class of conservative numerical methods for dispersive wave equations.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation A broad class of conservative numerical methods for dispersive wave equations

Reference 46

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source=pdf_text observed=2026-08-11T05:55:18.032048Z digest=sha256:d464053ab075f190e9b52c83d24562f4aa1fed892fc2874a576e269d29d519e5

Observation 455f6223-544b-4af3-8e60-89e740029311 · outbound

This paper cites Ketcheson.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Ketcheson

Reference 47

Resolution
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Observation 57113d02-7c26-4a5d-b265-c8e06b993b4f · outbound

This paper cites Difference Methods for Boundary-Value Problems.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Difference Methods for Boundary-Value Problems

Reference 48

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Observation 2cdb19f9-9650-4c9a-be6b-08cfa77cf117 · outbound

This paper cites Hyperbolic relaxation method for elliptic equations.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Hyperbolic relaxation method for elliptic equations

Reference 49

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source=pdf_text observed=2026-08-11T05:55:18.044662Z digest=sha256:0d00152375f1fe66d3c858eb21dd6d60df43ac8d1509d8b9f0399fd99f568da8

Observation f1505be9-dfc5-4446-828c-a323ee258fe6 · outbound

This paper cites Sch¨ utz and S.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Sch¨ utz and S

Reference 50

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Observation d33472ac-4d1d-4d1a-97b8-1ceb378a477a · outbound

This paper cites Review of summation-by-parts schemes for initial-boundary- value problems.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Review of summation-by-parts schemes for initial-boundary- value problems

Reference 51

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source=pdf_text observed=2026-08-11T05:55:18.052948Z digest=sha256:44bc27ed2c650464d0adc6329a5c1ff90145c1aeb8f99bde6969667ff89f7e5c

Observation 0ecb57f0-faa0-4ae6-9952-c9b1ad14ec49 · outbound

This paper cites Advection-diffusion-reaction equations: hyperbolization and high-order ADER discretizations.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Advection-diffusion-reaction equations: hyperbolization and high-order ADER discretizations

Reference 52

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source=pdf_text observed=2026-08-11T05:55:18.057415Z digest=sha256:2ff77fadcedd0502d2818d9674e604c1e94ba94e9dd0db9e51c6c9a166f29692

Observation 5b21264c-96a6-45b6-b94f-9909017670c1 · outbound

This paper cites Oliphant, Matt Haberland, Tyler Reddy, David Cour- napeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St´ efan J.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Oliphant, Matt Haberland, Tyler Reddy, David Cour- napeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St´ efan J

Reference 53

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raw_fallback, observed 2026-08-11T05:55:18.190375Z

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source=pdf_text observed=2026-08-11T05:55:18.061567Z digest=sha256:0e98ba3b78bd42874e9e2ffa875f9ef2df5d025559416403090f121c4a63146e

Observation 9b0026b9-a81f-47b6-b780-3602c5d19003 · outbound

This paper cites Nonlinear waves in integrable and nonintegrable systems.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Nonlinear waves in integrable and nonintegrable systems

Reference 54

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raw_fallback, observed 2026-08-11T05:55:18.173860Z

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source=pdf_text observed=2026-08-11T05:55:18.066033Z digest=sha256:323724cf8bf206e35bc7c317272bff513cf84eca9ce99c507ae90cd78a24fdeb

Observation d927f66b-2453-4f95-823f-904d779f0c4e · outbound

This paper cites Zeifang, J.

Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation Zeifang, J

Reference 55

Resolution
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raw_fallback, observed 2026-08-11T05:55:18.157646Z

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source=pdf_text observed=2026-08-11T05:55:18.070443Z digest=sha256:c98e3d90ed2ebf1c084fe4c63889c9d7f1469a4d45c7bfcaeda9d780f04d4acc

Pith citing papers

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