L. A. Kalyakin, “Perturbation of the Korteweg–de Vries soliton”, TMF, 92:1 (1992), 62–76; Theoret. and Math. Phys., 92:1 (1992), 736

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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 92, Number 1, Pages 62–76 (Mi tmf5661)

This article is cited in 19 scientific papers (total in 19 papers)

Perturbation of the Korteweg–de Vries soliton

L. A. Kalyakin

Institute of Mathematics of Bashkirian Scientific Centre, UB of USSR Academy of Sciences

Full-text PDF (1337 kB) Citations (19)

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Abstract: For an arbitrary perturbation operator, equations for the modulation of the parameters of the KdV soiiton are obtained. The asymptotic behavior of the first correction is investigated, and the influence of the leading term of this asymptotic behavior on the soliton phase shift is demonstrated.

Received: 21.03.1991

English version:
Theoretical and Mathematical Physics, 1992, Volume 92, Issue 1, Pages 736–747
DOI: https://doi.org/10.1007/BF01018701

Bibliographic databases:

Language: Russian

Citation: L. A. Kalyakin, “Perturbation of the Korteweg–de Vries soliton”, TMF, 92:1 (1992), 62–76; Theoret. and Math. Phys., 92:1 (1992), 736–747

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf5661

https://www.mathnet.ru/eng/tmf/v92/i1/p62

This publication is cited in the following 19 articles:

Sergiy LYASHKO, Valerii SAMOILENKO, Yuliia SAMOILENKO, Ihor GAPYAK, Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications 1, 2024, 1
L. A. Kalyakin, “Perturbation of a simple wave: from simulation to asymptotics”, Ufa Math. J., 15:3 (2023), 54–68
Georgy Omel'yanov, Complexity in Biological and Physical Systems - Bifurcations, Solitons and Fractals, 2018
G. Omel'yanov, “Propagation and interaction of solitons for nonintegrable equations”, Russ. J. Math. Phys., 23:2 (2016), 225
Georgy A. Omel'yanov, “Soliton‐type asymptotics for non‐integrable equations: a survey”, Math Methods in App Sciences, 38:10 (2015), 2062
Samoilenko V.H. Samoilenko Yu.I., “Two-Phase Solitonlike Solutions of the Cauchy Problem For a Singularly Perturbed Korteweg-de-Vries Equation With Variable Coefficients”, Ukr. Math. J., 65:11 (2014), 1681–1697
Koichi Narahara, “Characterization of partially dissipated solitons in a traveling-wave field-effect transistor”, Communications in Nonlinear Science and Numerical Simulation, 19:3 (2014), 494
Valeriy Hrygorovych Samoylenko, Yuliya Ivanivna Samoylenko, “Asymptotic multiphase Σ-solutions to the singularly perturbed Korteweg–de Vries equation with variable coefficients”, J Math Sci, 200:3 (2014), 358
S. A. Kordyukova, “Korteweg–de Vries hierarchy as an asymptotic limit of the Boussinesq system”, Theoret. and Math. Phys., 154:2 (2008), 250–259
A. Veksler, Y. Zarmi, “Perturbative Analysis of Wave Interaction in Nonlinear Systems”, Theoret. and Math. Phys., 144:2 (2005), 1227–1237
O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230
L. A. Kalyakin, “Asymptotic decay of solutions of the Liouville equation under perturbations”, Math. Notes, 68:2 (2000), 173–184
V. A. Lazarev, “Perturbation of a two-soliton solution of the Korteweg–de Vries equation in the case of close amplitudes”, Theoret. and Math. Phys., 118:3 (1999), 341–346
Kiselev, OM, “Perturbation theory for the Dirac equation in two-dimensional space”, Journal of Mathematical Physics, 39:4 (1998), 2333
L. A. Kalyakin, V. A. Lazarev, “Perturbation of the two-soliton solution of the KdV equation”, Theoret. and Math. Phys., 112:1 (1997), 866–874
R. R. Gadyl'shin, O. M. Kiselev, “On nonsolution structure of scattering data under perturbation of two-dimensional soliton for Davey–Stewartson equation II”, Theoret. and Math. Phys., 106:2 (1996), 167–173
L. A. Kalyakin, “Asymptotics of the first correction in the perturbation of the $N$ -soliton solution to the KdV equation”, Math. Notes, 58:2 (1995), 814–823
Y. Matsuno, “Multisoliton perturbation theory for the Benjamin-Ono equation and its application to real physical systems”, Phys. Rev. E, 51:2 (1995), 1471
Y. Matsuno, “Phase Shift of Interacting Algebraic Solitary Waves in a Two-Layer Fluid System”, Phys. Rev. Lett., 73:10 (1994), 1316

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

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