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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 165, Number 2, Pages 272–294
DOI: https://doi.org/10.4213/tmf6576
(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
References:
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.
Received: 26.02.2010
English version:
Theoretical and Mathematical Physics, 2010, Volume 165, Issue 2, Pages 1470–1489
DOI: https://doi.org/10.1007/s11232-010-0122-3
Bibliographic databases:
Document Type: Article
Language: Russian
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}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78651492533}
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  • https://doi.org/10.4213/tmf6576
  • https://www.mathnet.ru/eng/tmf/v165/i2/p272
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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