Eur. Phys. J. Appl. Phys. 52, 11301 (2010)
https://doi.org/10.1051/epjap/2010132

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

¹ Department of Photonics, National Sun Yat-Sen University, Kaohsiung, 804, Taiwan
² MEMS & Precision Machinery Research Center, College of Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, 807, Taiwan
³ Department of Applied Mathematics, National HsinChu University of Education, Hsinchu, 300, Taiwan

Corresponding author: chuntelee2000@googlemail.com

Received: 17 December 2009
Revised: 29 March 2010
Accepted: 23 July 2010
Published online: 17 September 2010

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.