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TMF, 2010, Volume 165, Number 2, Pages 272–294 (Mi tmf6576)  

This article is cited in 3 scientific papers (total in 3 papers)

New exact solutions with functional parameters of the Nizhnik–Veselov–Novikov equation with constant asymptotic values at infinity

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

Novosibirsk State Technical University

Abstract: We use the Zakharov–Manakov $\bar{\partial}$-dressing method to construct new classes of exact solutions with functional parameters of the hyperbolic and elliptic versions of the Nizhnik–Veselov–Novikov equation with constant asymptotic values at infinity. We show that the constructed solutions contain classes of multisoliton solutions, which at a fixed time are exact potentials of the perturbed telegraph equation {(}the perturbed string equation{\rm)} and the two-dimensional stationary Schrödinger equation. We interpret the stationary states of a microparticle in soliton-type potential fields physically in accordance with the constructed exact wave functions for the two-dimensional stationary Schrödinger equation.

Keywords: Nizhnik–Veselov–Novikov equation, solution with functional parameters, soliton, perturbed telegraph equation, two-dimensional stationary Schrödinger equation, transparent potential

DOI: https://doi.org/10.4213/tmf6576

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English version:
Theoretical and Mathematical Physics, 2010, 165:2, 1470–1489

Bibliographic databases:

Document Type: Article
Received: 26.02.2010

Citation: V. G. Dubrovskii, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions with functional parameters of the Nizhnik–Veselov–Novikov equation with constant asymptotic values at infinity”, TMF, 165:2 (2010), 272–294; Theoret. and Math. Phys., 165:2 (2010), 1470–1489

Citation in format AMSBIB
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\by V.~G.~Dubrovskii, A.~V.~Topovsky, M.~Yu.~Basalaev
\paper New exact solutions with functional parameters of the~Nizhnik--Veselov--Novikov equation with constant asymptotic values at infinity
\jour TMF
\yr 2010
\vol 165
\issue 2
\pages 272--294
\mathnet{http://mi.mathnet.ru/tmf6576}
\crossref{https://doi.org/10.4213/tmf6576}
\transl
\jour Theoret. and Math. Phys.
\yr 2010
\vol 165
\issue 2
\pages 1470--1489
\crossref{https://doi.org/10.1007/s11232-010-0122-3}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000286199500006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78651492533}


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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. V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions of two-dimensional integrable equations using the $\bar\partial$-dressing method”, Theoret. and Math. Phys., 167:3 (2011), 725–739  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. 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
    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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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