Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot | Paper Citation Record

Observation a3f7d64e-67a8-4aab-b798-704f77ef07fa · outbound

This paper cites Another simple separable solution of the NLSE (26) is ψ(s,t ) = 2 k sech (ks) exp(iDk 2t), (28) where the wavenumberk is constant.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Another simple separable solution of the NLSE (26) is ψ(s,t ) = 2 k sech (ks) exp(iDk 2t), (28) where the wavenumberk is constant

Reference 1

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Observation d36d72ad-5a4a-48c4-b294-33faf0602ecc · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 2

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Observation 0e355f43-2396-4b6a-bded-304c78f0443a · outbound

This paper cites From the Frenet-Serret curvature κ(s) = 2 τ0 sech(τ0s) and the constant torsion τ (s) = τ0, Hasimoto [10] was then able to construct a spatial curve r(s).

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot From the Frenet-Serret curvature κ(s) = 2 τ0 sech(τ0s) and the constant torsion τ (s) = τ0, Hasimoto [10] was then able to construct a spatial curve r(s)

Reference 3

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Observation d3852a09-56de-4f1a-93a3-9e33917d13f3 · outbound

This paper cites Betchov, On the curvature and torsion of an isolated vortex ﬁlament , J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Betchov, On the curvature and torsion of an isolated vortex ﬁlament , J

Reference 4

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Observation f1e2e9ef-d0f0-49bf-9450-0c0eb39f2e73 · outbound

This paper cites Here, the parameter m in Eq.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Here, the parameter m in Eq

Reference 5

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Observation 4c840d22-7d1c-4d7f-a11f-dca4976f2d9a · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 6

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Observation d98b7980-d434-4173-9949-33e22ee2d209 · outbound

This paper cites Nakayama, H.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Nakayama, H

Reference 7

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Observation 8f3c2078-eed0-40ca-8db9-bbe00bfa70d2 · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 8

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Observation e8e629e9-a459-459e-ba1e-2088b3317efe · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 9

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Observation c4e8249e-469e-4bb2-9112-60508e35df60 · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 10

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Observation 41944296-20af-49ad-90b7-7a381447275b · outbound

This paper cites 2) or in the range m < m− 0 ≃ − 4.7510 and q0 < 0 (i.e., region II in Fig.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot 2) or in the range m < m− 0 ≃ − 4.7510 and q0 < 0 (i.e., region II in Fig

Reference 11

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Observation b8a7635d-d353-4c9e-a990-9320d7a0cab9 · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 12

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Observation fb271a4f-cb4f-43e8-bae5-29c5bb4b4007 · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 13

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Observation ab1682c7-6c8f-4df1-b2c2-dc3c5f4febc1 · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 14

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Observation 44d5232a-6b17-4b6f-a94a-44535a894756 · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 15

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Observation 0e1ed51a-45f7-4d6e-b325-2d0a1d3dd7e2 · outbound

This paper cites (81), the phase integral (140) becomes θ(ξt) ≡ γξ t − i 2 ∫ ξt 0 ℘′(v +ω3)dw ℘(w +ω3) − ℘(v +ω3), (144) which has an identical form as Eq.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot (81), the phase integral (140) becomes θ(ξt) ≡ γξ t − i 2 ∫ ξt 0 ℘′(v +ω3)dw ℘(w +ω3) − ℘(v +ω3), (144) which has an identical form as Eq

Reference 16

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Observation abaf7b16-05e2-4c98-82c0-93a8dfe68524 · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 17

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Observation 2b586fed-dad0-4697-89d6-216d06de9292 · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 18

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Observation 36a704f8-4b2c-4299-a3b9-01a0bf327b1c · outbound

This paper cites Nizette and A.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Nizette and A

Reference 19

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Observation 66cb2b94-b954-4e0a-871f-48cfda8284b1 · outbound

This paper cites Singer, Lectures on elastic curves and rods , AIP Conf.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Singer, Lectures on elastic curves and rods , AIP Conf

Reference 20

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Observation 95de2ae9-2cff-41d6-b02d-f78507073bc7 · outbound

This paper cites Matsutani, Euler’s elastica and beyond , J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Matsutani, Euler’s elastica and beyond , J

Reference 21

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Observation aaaddeb8-97fd-4f9e-9a49-d43ea973e68c · outbound

This paper cites Uby, M.B.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Uby, M.B

Reference 22

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Observation 3030a724-86a2-4769-8076-8e00ba7b1da0 · outbound

This paper cites Ricca, Rediscovery of Da Rios equations , Nature 352, 561 (1991).

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Ricca, Rediscovery of Da Rios equations , Nature 352, 561 (1991)

Reference 23

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Observation ab51702f-2480-49a5-9c88-481a2d113b2c · outbound

This paper cites Ricca, The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex ﬁlament dy- namics, Fluid Dyn.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Ricca, The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex ﬁlament dy- namics, Fluid Dyn

Reference 24

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Observation 2d91b2e0-edba-4658-b339-bbc639ec1053 · outbound

This paper cites Salman, Breathers on quantized surperﬂuid vortices , Phys.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Salman, Breathers on quantized surperﬂuid vortices , Phys

Reference 25

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Observation e4e8fa5b-629d-4af4-92eb-baec977e6edd · outbound

This paper cites Kleckner and W.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Kleckner and W

Reference 26

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Observation dd9c4df8-b3ff-4f0f-bcf3-bcdfaacd0681 · outbound

This paper cites Hasimoto, Motion of a vortext ﬁlament and its relation to elastica , J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Hasimoto, Motion of a vortext ﬁlament and its relation to elastica , J

Reference 27

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Observation 62a8c6db-5ae8-4c80-9c89-b7f4649596ef · outbound

This paper cites Hasimoto, A soliton on a vortex ﬁlament , J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Hasimoto, A soliton on a vortex ﬁlament , J

Reference 28

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Observation 5d9fa741-39e2-478b-9552-0226889618f9 · outbound

This paper cites Lamb, Jr., Solitons and the motion of helical curves , Phys.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Lamb, Jr., Solitons and the motion of helical curves , Phys

Reference 29

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Observation 49225aa9-1fde-49d5-a155-e3a9a13c64f7 · outbound

This paper cites Lamb, Jr., Solitons on moving space curves , J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Lamb, Jr., Solitons on moving space curves , J

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:36.836263Z

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Observation f5d530e6-e655-4124-a0df-4383834274fd · outbound

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Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 31

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Observation df1f162b-c23f-4ee6-82be-8c27d7f4d350 · outbound

This paper cites Kida, A vortex ﬁlament moving without change of form, J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Kida, A vortex ﬁlament moving without change of form, J

Reference 32

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Observation f7e21320-5a31-4ae3-ae7e-6fc396f117df · outbound

This paper cites Hasimoto, Elementary aspects of vortex motion , Fluid Dyn.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Hasimoto, Elementary aspects of vortex motion , Fluid Dyn

Reference 33

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Observation 3a3e9d1b-5ee2-42b9-b102-bd351af3a058 · outbound

This paper cites Balakrishnan and R.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Balakrishnan and R

Reference 34

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Observation 58a9821e-94bb-4349-9fca-62e42292099e · outbound

This paper cites Zakharov and A.B.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Zakharov and A.B

Reference 35

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Observation f5772027-1572-48a8-9444-1a082328f159 · outbound

This paper cites Ablowitz and B.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Ablowitz and B

Reference 36

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Observation 8ced3104-c7e1-4bb1-b456-8d5153419111 · outbound

This paper cites Here, the complete elliptic integrals K(m) and E(m) of the ﬁrst and second kinds are deﬁned in Eqs.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Here, the complete elliptic integrals K(m) and E(m) of the ﬁrst and second kinds are deﬁned in Eqs

Reference 37

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Observation 895bdf57-42ad-4852-b897-d19c7013ffba · outbound

This paper cites Dewar, A Lagrangian theory for nonlinear wave packets in a collisionless plasma , J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Dewar, A Lagrangian theory for nonlinear wave packets in a collisionless plasma , J

Reference 38

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Observation 5804cd33-3a56-4613-bc16-410beb5baac7 · outbound

This paper cites Dysthe and H.L.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Dysthe and H.L

Reference 39

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Observation 0b79d342-c595-4657-b821-e6ed1cbc577e · outbound

This paper cites Dysthe, E.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Dysthe, E

Reference 40

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Observation beaa9dd9-af35-40d4-85c8-f4a606b16411 · outbound

This paper cites Peregrine, Water waves, nonlinear Schr¨ odinger equations and their solutions , J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Peregrine, Water waves, nonlinear Schr¨ odinger equations and their solutions , J

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:37.469148Z

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Observation c16055dc-5f7f-48ee-8da3-5bb1e94518ee · outbound

This paper cites Sulem and P.L.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Sulem and P.L

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:37.560935Z

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Observation 2f1725a6-4744-4487-8627-a082a27c5b84 · outbound

This paper cites Dysthe, H.E.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Dysthe, H.E

Reference 43

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Observation 10a5b7d5-e4b7-40f8-9010-fd8c00546f3b · outbound

This paper cites Akbari-Moghanjoughi, Traveling wave solutions of the nonlinear Schr¨ odinger equation, Phys.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Akbari-Moghanjoughi, Traveling wave solutions of the nonlinear Schr¨ odinger equation, Phys

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Observation 630e2fac-cb71-40e2-abe8-3c76a66b863a · outbound

This paper cites The nonlinear Schr\"odinger equation: A mathematical model with its wide-ranging applications.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot The nonlinear Schr\"odinger equation: A mathematical model with its wide-ranging applications

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Observation afd01c62-65f6-4761-a322-a7d16d2ea5a1 · outbound

This paper cites Carter, C.W.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Carter, C.W

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.086693Z

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Observation fc32e9b6-bba9-4c6e-a2af-d50ddbdbeb87 · outbound

This paper cites Smondyrev, P.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Smondyrev, P

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.171468Z

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Observation 8693583c-e85f-48c6-a392-4e2744c381ad · outbound

This paper cites Salman, Multiple breathers on a vortex ﬁlament , J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Salman, Multiple breathers on a vortex ﬁlament , J

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Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.227392Z

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Observation 93914a78-fb30-4c4d-ac64-917762bb69b4 · outbound

This paper cites Langer and D.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Langer and D

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.335541Z

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Observation c0794a57-60f0-4e46-83f7-75478a0f9fcd · outbound

This paper cites Langer and D.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Langer and D

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.429884Z

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Observation a19f5cf7-7ad4-4608-9757-5b128170f0b5 · outbound

This paper cites Langer and D.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Langer and D

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.522148Z

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Observation e76f0ed3-503c-406b-8403-f4de3470293f · outbound

This paper cites Barros, A.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Barros, A

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.717254Z

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Observation a350ad16-725a-4814-9bd7-66bd22be59e8 · outbound

This paper cites an unresolved cited work.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.797833Z

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Observation 1243fab7-b992-4b00-9c24-b98bfc5b6cda · outbound

This paper cites Reinhart and P.L.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Reinhart and P.L

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:38.939808Z

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Observation 690d8829-8e98-4e55-8ff2-5fd0ed50c612 · outbound

This paper cites Milne-Thomson, Jacobi Elliptic Functions and Theta Functions & Elliptic Integrals , in Handbook of mathematical functions, M.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Milne-Thomson, Jacobi Elliptic Functions and Theta Functions & Elliptic Integrals , in Handbook of mathematical functions, M

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.059642Z

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Observation d6b2cb83-12ca-4164-80b8-f3765c2f5d7b · outbound

This paper cites Pfeﬀerl´ e, L.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Pfeﬀerl´ e, L

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.098601Z

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Observation d8ce8849-a952-4891-bafc-aefe3538cb5b · outbound

This paper cites Equivalent elastica knots.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Equivalent elastica knots

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.175800Z

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Observation 9f7b1387-7628-41e4-a1c3-c619203368b1 · outbound

This paper cites Cary and A.J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Cary and A.J

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.293457Z

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Observation e31cba78-1259-4066-8765-79762c59f659 · outbound

This paper cites Dysthe and K.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Dysthe and K

Reference 59

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Observation 0ae26e5f-39a0-46c0-aecd-d30afe6dd586 · outbound

This paper cites Chabchoub, B.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Chabchoub, B

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.456512Z

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Observation 3e4c4b38-8ef5-416d-8e06-d0b0fe91dcce · outbound

This paper cites Akhmediev and V.I.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Akhmediev and V.I

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.530936Z

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Observation 3f81639b-786c-47d3-9f89-d03bf03b483d · outbound

This paper cites Akhmediev, A.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Akhmediev, A

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.569836Z

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Observation 9e97257a-ac58-4194-a679-3a6d83cf2a96 · outbound

This paper cites Akhmediev, J.M.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Akhmediev, J.M

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.621460Z

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Observation 34d0b156-fe7d-46e9-a2a1-889c71b52b93 · outbound

This paper cites Ma, Studies Appl.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Ma, Studies Appl

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.677590Z

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Observation 4869cf4c-c79b-4607-b508-b9e45cf9b7f6 · outbound

This paper cites Ince, V.—The Periodic Lam´ e Functions, Proc.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Ince, V.—The Periodic Lam´ e Functions, Proc

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.732675Z

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Observation 1a39403f-421f-43bb-9945-3906365247b2 · outbound

This paper cites Erd´ elyi,XIII.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Erd´ elyi,XIII

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.790921Z

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Observation 9b8a9a11-0b4d-40c7-b16d-ff752e489839 · outbound

This paper cites Volkmer, Lam´ e Functions, in NIST Handbook of Mathematical Functions, F.W.J.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Volkmer, Lam´ e Functions, in NIST Handbook of Mathematical Functions, F.W.J

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.874030Z

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Observation 315b0a10-2376-49fd-a114-ef57af023907 · outbound

This paper cites an unresolved cited work.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Unresolved cited work

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.912117Z

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Observation 48b56a32-a5f6-41fc-abb9-e202e2d4a92d · outbound

This paper cites Hasegawa, An historical review of application of op- tical solitons for high speed communications , Chaos 10, 475 (2000).

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Hasegawa, An historical review of application of op- tical solitons for high speed communications , Chaos 10, 475 (2000)

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Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.929105Z

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Observation 2e8013c3-dd5a-4dc3-8338-ecb936498928 · outbound

This paper cites Hasegawa, Optical soliton: Review of its discovery and applications in ultra-high-speed communications , Fron- tiers in Physics 10, 1044845 (2022).

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Hasegawa, Optical soliton: Review of its discovery and applications in ultra-high-speed communications , Fron- tiers in Physics 10, 1044845 (2022)

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Observation e31c3c4f-3027-4aa3-a868-a549d8151820 · outbound

This paper cites Bohm, A Suggested Interpretation of the Quantum Theory in Terms of “Hidden ” Variables.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Bohm, A Suggested Interpretation of the Quantum Theory in Terms of “Hidden ” Variables

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:39.993168Z

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Observation 0c914fd5-791a-430c-953b-6965d1455cb2 · outbound

This paper cites Brizard, A primer on elliptic functions with applica- tions in classical mechanics , Eur.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Brizard, A primer on elliptic functions with applica- tions in classical mechanics , Eur

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Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:40.004258Z

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Observation 597fc256-c72d-4d75-b4fc-903107345d93 · outbound

This paper cites Brizard, Scenarios for magnetic X-point collapse in 2D dissipationless extended magnetohydrodynamics , Comm.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Brizard, Scenarios for magnetic X-point collapse in 2D dissipationless extended magnetohydrodynamics , Comm

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:40.066061Z

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Observation a30b9551-d957-42a1-8dd2-f625cdd2c768 · outbound

This paper cites Reinhart and P.L.

Nonlinear Schr\"{o}dinger equation on a closed 3D elastica knot Reinhart and P.L

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:40.123375Z

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