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Quasi-solitons of the two-mode Korteweg-de Vries equation

Published online by Cambridge University Press:  17 September 2010

C.-C. Lee ,
C.-T. Lee ,
J.-L. Liu  and
W.-Y. Huang
C.-C. Lee
Affiliation:
Department of Photonics, National Sun Yat-Sen University, Kaohsiung, 804, Taiwan
C.-T. Lee*
Affiliation:
MEMS & Precision Machinery Research Center, College of Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, 807, Taiwan
J.-L. Liu
Affiliation:
Department of Applied Mathematics, National HsinChu University of Education, Hsinchu, 300, Taiwan
W.-Y. Huang
Affiliation:
Department of Photonics, National Sun Yat-Sen University, Kaohsiung, 804, Taiwan
*
[email protected]
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Abstract

The two-mode Korteweg-de Vries equation (TMKdV) was proposed to describe thepropagation of nonlinear waves of two different wave modes simultaneously.However, the existence of multi-soliton solutions is still unknown. In thisletter we present two Hamiltonians, the conservation laws, and a Miura-liketransformation of the equation. We show that the TMKdV equation has“quasi-soliton” behaviour in which waves moving in the same direction passthrough each other almost without change of their wave forms except forphase shifts.

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 52 , Issue 1 , October 2010 , 11301
Copyright
© EDP Sciences, 2010

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