### 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 |
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Pages (from-to) | 99-105 |

Number of pages | 7 |

Journal | Czechoslovak Journal of Physics |

Volume | 53 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2003 |

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### 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)

### Cite this

**Lie group of transformations for a KdV-Boussinesq equation.** / Krishnan, E. V.; Khan, Q. J A.

Research output: Contribution to journal › Article

*Czechoslovak Journal of Physics*, vol. 53, no. 2, pp. 99-105. https://doi.org/10.1023/A:1022326900538

}

TY - JOUR

T1 - Lie group of transformations for a KdV-Boussinesq equation

AU - Krishnan, E. V.

AU - Khan, Q. J A

PY - 2003/2

Y1 - 2003/2

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.

KW - Explode decay mode solutions

KW - Jacobian elliptic functions

KW - KdV-Boussinesq equation

KW - Solitary wave solutions

KW - Travelling wave solutions

UR - http://www.scopus.com/inward/record.url?scp=3543016189&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3543016189&partnerID=8YFLogxK

U2 - 10.1023/A:1022326900538

DO - 10.1023/A:1022326900538

M3 - Article

VL - 53

SP - 99

EP - 105

JO - Czechoslovak Journal of Physics

JF - Czechoslovak Journal of Physics

SN - 0011-4626

IS - 2

ER -