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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 3, Pages 435–445 (Mi zvmmf10171)  

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

Numerical analysis of soliton solutions of the modified Korteweg–de Vries–sine-Gordon equation

S. P. Popov

Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: Multisoliton solutions of the modified Korteweg–de Vries–sine-Gordon equation (mKdV-SG) are found numerically by applying the quasi-spectral Fourier method and the fourth-order Runge–Kutta method. The accuracy and features of the approach are determined as applied to problems with initial data in the form of various combinations of perturbed soliton distributions. Three-soliton solutions are obtained, and the generation of kinks, breathers, wobblers, perturbed kinks, and nonlinear oscillatory waves is studied.

Key words: mKdV equation, SG equation, mKdV-SG equation, SGmKdV equation, SPE equation, kink, antikink, breather, wobbler, soliton, multisoliton interaction.

DOI: https://doi.org/10.7868/S004446691503014X

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:3, 437–446

Bibliographic databases:

UDC: 519.634
MSC: 65M70
Received: 15.05.2014
Revised: 15.10.2014

Citation: S. P. Popov, “Numerical analysis of soliton solutions of the modified Korteweg–de Vries–sine-Gordon equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015), 435–445; Comput. Math. Math. Phys., 55:3 (2015), 437–446

Citation in format AMSBIB
\by S.~P.~Popov
\paper Numerical analysis of soliton solutions of the modified Korteweg--de Vries--sine-Gordon equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 3
\pages 435--445
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 3
\pages 437--446

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    This publication is cited in the following articles:
    1. S. Terniche, H. Leblond, D. Mihalache, A. Kellou, “Few-cycle optical solitons in linearly coupled waveguides”, Phys. Rev. A, 94:6 (2016), 063836  crossref  isi  elib  scopus
    2. M. Baccouch, “Optimal energy-conserving local discontinuous Galerkin method for the one-dimensional sine-Gordon equation”, Int. J. Comput. Math., 94:2 (2017), 316–344  crossref  mathscinet  zmath  isi  scopus
    3. H. Leblond, D. Kremer, D. Mihalache, “Few-cycle spatiotemporal optical solitons in waveguide arrays”, Phys. Rev. A, 95:4 (2017), 043839  crossref  mathscinet  isi
    4. D. Mihalache, “Multidimensional localized structures in optical and matter-wave media: a topical survey of recent literature”, Rom. Rep. Phys., 69:1 (2017), 403  isi
    5. S. P. Popov, “New compacton solutions of an extended Rosenau–Pikovsky equation”, Comput. Math. Math. Phys., 57:9 (2017), 1540–1549  mathnet  crossref  crossref  isi  elib  elib
    6. M. Baccouch, “Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation in one space dimension”, J. Comput. Appl. Math., 333 (2018), 292–313  crossref  mathscinet  zmath  isi
    7. S. P. Popov, “Compactons and Riemann waves of an extended modified Korteweg–de Vries equation with nonlinear dispersion”, Comput. Math. Math. Phys., 58:3 (2018), 437–448  mathnet  crossref  crossref  isi  elib
    8. H. Leblond, D. Mihalache, “Ultrashort spatiotemporal optical solitons in waveguide arrays: the effect of combined linear and nonlinear couplings”, J. Phys. A-Math. Theor., 51:43 (2018), 435202  crossref  isi  scopus
    9. Baccouch M., “Optimal Error Estimates of the Local Discontinuous Galerkin Method For the Two-Dimensional Sine-Gordon Equation on Cartesian Grids”, Int. J. Numer. Anal. Model., 16:3 (2019), 436–462  mathscinet  isi
    10. Wazwaz A.-M., Kaur L., “Complex Simplified Hirota'S Forms and Lie Symmetry Analysis For Multiple Real and Complex Soliton Solutions of the Modified Kdv-Sine-Gordon Equation”, Nonlinear Dyn., 95:3 (2019), 2209–2215  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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