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TMF, 2007, Volume 151, Number 3, Pages 380–390 (Mi tmf6053)  

This article is cited in 1 scientific paper (total in 1 paper)

New solutions of the Schwarzian Korteweg–de Vries equation in $2{+}1$ dimensions based on weak symmetries

M. L. Gandarias, M. S. Bruzón

Universidad de Cadiz

Abstract: We consider the $(2+1)$-dimensional integrable Schwarzian Korteweg–de Vries equation. Using weak symmetries, we obtain a system of partial differential equations in $1+1$ dimensions. Further reductions lead to second-order ordinary differential equations that provide new solutions expressible in terms of known functions. These solutions depend on two arbitrary functions and one arbitrary solution of the Riemann wave equation and cannot be obtained by classical or nonclassical symmetries. Some of the obtained solutions of the Schwarzian Korteweg–de Vries equation exhibit a wide variety of qualitative behaviors; traveling waves and soliton solutions are among the most interesting.

Keywords: weak symmetry, partial differential equation, solitary wave

DOI: https://doi.org/10.4213/tmf6053

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English version:
Theoretical and Mathematical Physics, 2007, 151:3, 752–761

Bibliographic databases:


Citation: M. L. Gandarias, M. S. Bruzón, “New solutions of the Schwarzian Korteweg–de Vries equation in $2{+}1$ dimensions based on weak symmetries”, TMF, 151:3 (2007), 380–390; Theoret. and Math. Phys., 151:3 (2007), 752–761

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. Aslan I., “Analytic investigation of the (2+1)-dimensional Schwarzian Korteweg-de Vries equation for traveling wave solutions”, Applied Mathematics and Computation, 217:12 (2011), 6013–6017  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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