Paper Citation Record · LEDGER

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation

As of 23 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 1 inbound Pith citation observation for arXiv:2505.03271.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.03271 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:04:53.104410Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-13T02:13:51.480364Z

measured 1 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-05T02:28:24.338817Z

Reference resolution

25 of 25 outbound references displayed

verified exact1
verified fuzzy21
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
pith, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation f2bf17b1-1c56-4647-ac78-a923b5f0995d · outbound

This paper cites Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-16T00:04:53.207831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 307233e7-c2c4-488e-be3b-23bcc95dcaeb · outbound

This paper cites an unresolved cited work.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:04:53.652551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1c5a3dba-8b77-4599-bf44-9fffc3055ca4 · outbound

This paper cites Continuous approximation of brea thers in one-and two-dimensional DNLS lattices.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Continuous approximation of brea thers in one-and two-dimensional DNLS lattices

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.642443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a49f7c53-e50e-48ec-b77a-3467fbafb48e · outbound

This paper cites Existenc e and stability of ground states for fully discrete approximations of the nonlinear Schrödinger equa tion.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Existenc e and stability of ground states for fully discrete approximations of the nonlinear Schrödinger equa tion

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.632525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation db9a1e4a-f6d1-4243-b055-8dae0c2f2f3c · outbound

This paper cites On the Hamilt onian interpolation of near-to-the identity sym- plectic mappings with application to symplectic integrati on algorithms.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation On the Hamilt onian interpolation of near-to-the identity sym- plectic mappings with application to symplectic integrati on algorithms

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.622989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 46ea2888-2fa5-4777-8e9e-41b5806d8ba3 · outbound

This paper cites Existence and stability of traveling waves for discrete nonlinear Schrödinger equations over long times.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Existence and stability of traveling waves for discrete nonlinear Schrödinger equations over long times

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.613085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a035b0d9-53af-494e-937c-b99cd01f4522 · outbound

This paper cites Polynomials and multili near mappings in topological vector-spaces.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Polynomials and multili near mappings in topological vector-spaces

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.603305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dc17fe7c-a483-40c7-997f-f5dfff16994e · outbound

This paper cites Symme tric exponential integrators with an appli- cation to the cubic Schrödinger equation.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Symme tric exponential integrators with an appli- cation to the cubic Schrödinger equation

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.592861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 52b434b2-5e05-49fe-b9f3-506bed2478e6 · outbound

This paper cites Courant, K.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Courant, K

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.582690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b80e416e-92ff-420d-92fe-9f6e750908ef · outbound

This paper cites Modiﬁed energy for spl it-step methods applied to the linear Schrödinger equation.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Modiﬁed energy for spl it-step methods applied to the linear Schrödinger equation

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.573082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 97256ed2-3f49-4fb1-88d0-6d5be883a1c7 · outbound

This paper cites Geometric numerical integration and Schrödinger equations , volume 15.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Geometric numerical integration and Schrödinger equations , volume 15

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.562514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 19773e34-d4b7-440e-9d24-198b8296e834 · outbound

This paper cites Pla ne wave stability of the split-step Fourier method for the nonlinear Schrödinger equation.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Pla ne wave stability of the split-step Fourier method for the nonlinear Schrödinger equation

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.552712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c7236b0e-3d9e-4f63-b389-b29aca891e1c · outbound

This paper cites Hamiltonian interpolat ion of splitting approximations for nonlinear PDEs.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Hamiltonian interpolat ion of splitting approximations for nonlinear PDEs

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.542048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a8db4d91-a135-4eb7-8441-27969ea0942d · outbound

This paper cites Birkhoﬀ n ormal form for splitting methods applied to semi linear Hamiltonian PDEs.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Birkhoﬀ n ormal form for splitting methods applied to semi linear Hamiltonian PDEs

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.531130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 467ea4b3-d45d-431c-857a-00cfeeba5e58 · outbound

This paper cites Birkhoﬀ n ormal form for splitting methods applied to semi linear Hamiltonian PDEs.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Birkhoﬀ n ormal form for splitting methods applied to semi linear Hamiltonian PDEs

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.520496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9831b531-6c58-488a-ab79-6dd3c0733db3 · outbound

This paper cites Note on the derivatives with res pect to a parameter of the solutions of a system of diﬀerential equations.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Note on the derivatives with res pect to a parameter of the solutions of a system of diﬀerential equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.510329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 233a2796-e836-46b1-ad04-17090b22b263 · outbound

This paper cites Hairer, C.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Hairer, C

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.499802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0e44f5dc-1c4b-4d7e-8078-86082ba0d337 · outbound

This paper cites The Gronwall Inequality.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation The Gronwall Inequality

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.488558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5c2f4b03-01f0-491f-ae14-25cbfa40bbf3 · outbound

This paper cites The discrete nonlinear Schrödinger equation: mathematical analysis, numerical computations and physical perspectives , volume 232.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation The discrete nonlinear Schrödinger equation: mathematical analysis, numerical computations and physical perspectives , volume 232

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.477042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fdccf6bf-74fe-4301-8af6-57e08a4b0a45 · outbound

This paper cites Bridging the g ap: symplecticity and low regularity in Runge– Kutta resonance-based schemes.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Bridging the g ap: symplecticity and low regularity in Runge– Kutta resonance-based schemes

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.465957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c6420d94-07e2-43b4-be52-4c4153fa9bd0 · outbound

This paper cites Marsden and T.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Marsden and T

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.367824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f55ff2da-8cdc-4674-af59-d3a33a8d937b · outbound

This paper cites Métodos simplécticos desarrollables en P-series.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Métodos simplécticos desarrollables en P-series

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.320221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5d34ab55-e3d9-4d68-acc3-89a38bb460fb · outbound

This paper cites an unresolved cited work.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:04:53.308889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 07fe81c3-0133-4786-9c1d-d16ff6a462c1 · outbound

This paper cites Implicit-explicit varia tional integration of highly oscillatory problems.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Implicit-explicit varia tional integration of highly oscillatory problems

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:04:53.296799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 420f3cec-7953-4e9f-b35a-50d596982c9c · outbound

This paper cites an unresolved cited work.

Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:04:53.280561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

Observation c4cf6488-95a8-475f-a077-93b422f36166 · inbound

Backward error analysis for matrix discretizations of 2-D Euler equations cites this paper.

Backward error analysis for matrix discretizations of 2-D Euler equations Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-07-13T02:19:16.512846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.