Lie group of transformations for a KdV-Boussinesq equation

E. V. Krishnan; Q. J A Khan

doi:10.1023/A:1022326900538

Lie group of transformations for a KdV-Boussinesq equation

E. V. Krishnan^*, Q. J A Khan

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider a combined Korteweg-deVries and Boussinesq equation governing long surface waves in shallow water. Considering traveling wave solutions, the basic equations will be reduced to a second order ordinary differential equation. Using the Lie group of transformations we reduce it to a first order ordinary differential equation and employ a direct method to derive its periodic solutions in terms of Jacobian elliptic functions and their corresponding solitary wave and explode decay mode solutions.

Original language	English
Pages (from-to)	99-105
Number of pages	7
Journal	Czechoslovak Journal of Physics
Volume	53
Issue number	2
DOIs	https://doi.org/10.1023/A:1022326900538
Publication status	Published - Feb 2003

Keywords

Explode decay mode solutions
Jacobian elliptic functions
KdV-Boussinesq equation
Solitary wave solutions
Travelling wave solutions

ASJC Scopus subject areas

Physics and Astronomy(all)

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N2 - We consider a combined Korteweg-deVries and Boussinesq equation governing long surface waves in shallow water. Considering traveling wave solutions, the basic equations will be reduced to a second order ordinary differential equation. Using the Lie group of transformations we reduce it to a first order ordinary differential equation and employ a direct method to derive its periodic solutions in terms of Jacobian elliptic functions and their corresponding solitary wave and explode decay mode solutions.

AB - We consider a combined Korteweg-deVries and Boussinesq equation governing long surface waves in shallow water. Considering traveling wave solutions, the basic equations will be reduced to a second order ordinary differential equation. Using the Lie group of transformations we reduce it to a first order ordinary differential equation and employ a direct method to derive its periodic solutions in terms of Jacobian elliptic functions and their corresponding solitary wave and explode decay mode solutions.

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KW - Jacobian elliptic functions

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KW - Solitary wave solutions

KW - Travelling wave solutions

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