Resonant behavior of multiple wave solutions to a Hirota bilinear equation

For the exponential traveling wave solutions to the Hirota bilinear equations, a sufficient and necessary criterion for the existence of linear superposition principle has been given. Motivated by this criterion, we propose a new Hirota bilinear equation via using a multivariate polynomial. Applying...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 72; no. 5; pp. 1225 - 1229
Main Authors Gao, Li-Na, Zhao, Xue-Ying, Zi, Yao-Yao, Yu, Jun, Lü, Xing
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2016
Subjects
Criteria
Hirota bilinear equation
Linear superposition principle
Mathematical analysis
Mathematical models
Multiple wave solution
Polynomials
Resonant solution
Traveling waves
Hirota bilinear equation
Resonant solution
Linear superposition principle
Multiple wave solution
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ISSN0898-1221
1873-7668
DOI10.1016/j.camwa.2016.06.008

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Summary:For the exponential traveling wave solutions to the Hirota bilinear equations, a sufficient and necessary criterion for the existence of linear superposition principle has been given. Motivated by this criterion, we propose a new Hirota bilinear equation via using a multivariate polynomial. Applying the linear superposition principle to this new Hirota bilinear equation, we finally find two types of resonant multiple wave solutions, among which, the resonant three-wave solutions are illustrated with three-dimensional plots.
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2016.06.008