Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

Full text: PDF file (513 kB)
References: PDF file   HTML file

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
\Bibitem{Pop15}
\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
\mathnet{http://mi.mathnet.ru/zvmmf10171}
\crossref{https://doi.org/10.7868/S004446691503014X}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3334443}
\zmath{https://zbmath.org/?q=an:06458220}
\elib{https://elibrary.ru/item.asp?id=22995535}
\transl
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 3
\pages 437--446
\crossref{https://doi.org/10.1134/S0965542515030136}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000352701800008}
\elib{https://elibrary.ru/item.asp?id=24023930}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928155853}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10171
  • http://mi.mathnet.ru/eng/zvmmf/v55/i3/p435

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    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
    Number of views:
    This page:223
    Full text:67
    References:42
    First page:9

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021