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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
*
chuntelee2000@googlemail.com
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Abstract

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