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 | |
| 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.
In: Czechoslovak Journal of Physics, Vol. 53, No. 2, 02.2003, p. 99-105.Research output: Contribution to journal › Article
}
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 -