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TMF, 2011, Volume 167, Number 3, Pages 377–393 (Mi tmf6648)  

This article is cited in 5 scientific papers (total in 5 papers)

New exact solutions of two-dimensional integrable equations using the $\bar\partial$-dressing method

V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev

Novosibirsk State Technical University, Novosibirsk, Russia

Abstract: We review new classes of exact solutions with functional parameters with constant asymptotic values at infinity of the Nizhnik–Veselov–Novikov equation and new classes of exact solutions with functional parameters of two-dimensional generalizations of the Kaup–Kupershmidt and Sawada–Kotera equations, constructed using the Zakharov–Manakov $\bar\partial$-dressing method. We present subclasses of multisoliton and periodic solutions of these equations and give examples of linear superpositions of exact solutions of the Nizhnik–Veselov–Novikov equation.

Keywords: Nizhnik–Veselov–Novikov equation, two-dimensional Kaup–Kupershmidt equation, two-dimensional Sawada–Kotera equation, solutions with functional parameters, two-dimensional stationary Schrödinger equation, soliton, transparent potential

DOI: https://doi.org/10.4213/tmf6648

Full text: PDF file (467 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 167:3, 725–739

Bibliographic databases:

Document Type: Article
Received: 23.06.2011

Citation: V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions of two-dimensional integrable equations using the $\bar\partial$-dressing method”, TMF, 167:3 (2011), 377–393; Theoret. and Math. Phys., 167:3 (2011), 725–739

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dubrovsky V.G., Topovsky A.V., “About Simple Nonlinear and Linear Superpositions of Special Exact Solutions of Veselov-Novikov Equation”, J. Math. Phys., 54:3 (2013), 033509  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Adem A.R., Khalique Ch.M., “Exact Solutions and Conservation Laws of a Two-Dimensional Integrable Generalization of the Kaup-Kupershmidt Equation”, J. Appl. Math., 2013, 647313  crossref  mathscinet  zmath  isi  elib  scopus
    3. Dubrovsky V.G., Topovsky A.V., “About Linear Superpositions of Special Exact Solutions of Nizhnik-Veselov-Novikov Equation”, Physics and Mathematics of Nonlinear Phenomena 2013, Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012011  crossref  isi  scopus
    4. Chang J.-H., “The interactions of solitons in the Novikov–Veselov equation”, Appl. Anal., 95:6 (2016), 1370–1388  crossref  mathscinet  zmath  isi  elib  scopus
    5. Adem A.R., Lu X., “Travelling wave solutions of a two-dimensional generalized Sawada–Kotera equation”, Nonlinear Dyn., 84:2 (2016), 915–922  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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