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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 3, Pages 377–393
DOI: https://doi.org/10.4213/tmf6648 (Mi tmf6648) 		 
This article is cited in 11 scientific papers (total in 11 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
Full-text PDF (467 kB) Citations (11)
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DOI: https://doi.org/10.4213/tmf6648
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.
Received: 23.06.2011
English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 3, Pages 725–739
DOI: https://doi.org/10.1007/s11232-011-0057-3
Bibliographic databases:
Document Type: Article
Language: Russian
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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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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