I. T. Habibullin, A. G. Shagalov, “Numerical realization of the inverse scattering method”, TMF, 83:3 (1990), 323–333; Theoret. and Math. Phys., 83:3 (1990), 565

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Teoreticheskaya i Matematicheskaya Fizika, 1990, Volume 83, Number 3, Pages 323–333 (Mi tmf5805)

This article is cited in 10 scientific papers (total in 10 papers)

Numerical realization of the inverse scattering method

I. T. Habibullin, A. G. Shagalov

Full-text PDF (1117 kB) Citations (10)

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Abstract: A method of solving the Cauchy problem for integrable equations that is specially suited to the application of numerical methods is proposed. The dynamics of singular solutions in a differential-difference analog of the nonlinear Schrödinger equation is investigated in detail.

Received: 03.05.1989

English version:
Theoretical and Mathematical Physics, 1990, Volume 83, Issue 3, Pages 565–573
DOI: https://doi.org/10.1007/BF01018024

Bibliographic databases:

Language: Russian

Citation: I. T. Habibullin, A. G. Shagalov, “Numerical realization of the inverse scattering method”, TMF, 83:3 (1990), 323–333; Theoret. and Math. Phys., 83:3 (1990), 565–573

Citation in format AMSBIB

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\pages 323--333

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\jour Theoret. and Math. Phys.

\yr 1990

\vol 83

\issue 3

\pages 565--573

\crossref{https://doi.org/10.1007/BF01018024}

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Linking options:

https://www.mathnet.ru/eng/tmf5805

https://www.mathnet.ru/eng/tmf/v83/i3/p323

This publication is cited in the following 10 articles:

V. M. Adukov, G. Mishuris, “Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method”, Proc. R. Soc. A., 479:2269 (2023)
V. M. Adukov, “Normalization of Wiener–Hopf factorization for $2\times 2$ matrix functions and its application”, Ufa Math. J., 14:4 (2022), 1–13
S. N. Kiyasov, “Approximate factorization for a class of second-order matrix functions”, Lobachevskii J Math, 38:6 (2017), 1131
S. N. Kiyasov, “Priblizhennaya faktorizatsiya odnogo klassa matrits-funktsii vtorogo poryadka”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2016, 511–529
Charles L Epstein, Jeremy Magland, “The hard pulse approximation for the AKNS (2 × 2)-system”, Inverse Problems, 25:10 (2009), 105006
F. Musso, A. B. Shabat, “Elementary Darboux Transformations and Factorization”, Theoret. and Math. Phys., 144:1 (2005), 1004–1013
Michael Öster, Yuri B. Gaididei, Magnus Johansson, Peter L. Christiansen, “Nonlocal and nonlinear dispersion in a nonlinear Schrödinger-type equation: exotic solitons and short-wavelength instabilities”, Physica D: Nonlinear Phenomena, 198:1-2 (2004), 29
A. G. SHAGALOV, “SYMPLECTIC NUMERICAL METHODS IN DYNAMICS OF NONLINEAR WAVES”, Int. J. Mod. Phys. C, 10:05 (1999), 967
V. V. Konotop, “Lattice dark solitons in the linear potential”, Theoret. and Math. Phys., 99:3 (1994), 687–691
B. I. Suleimanov, I. T. Habibullin, “Symmetries of Kadomtsev–Petviashvili equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes”, Theoret. and Math. Phys., 97:2 (1993), 1250–1258

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	84
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