Hostname: page-component-7dd5485656-npwhs Total loading time: 0 Render date: 2025-10-31T09:02:07.657Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Korsunsky, S.V., Phys. Lett. A 185, 174 (1994) CrossRef
C.T. Lee, Ph.D. thesis, Oxford University, 2007
Hirota, R., Satsuma, J., Phys. Lett. A 85, 407 (1981) CrossRef
Gear, J.A., Grimshaw, R., Stud. Appl. Math. 70, 235 (1984) CrossRef
T. Taniuti, Reductive perturbation method for quasi one-dimensional wave propagation, Nonlinear wave motion (Longman, Boston, 1989)
Magri, F., J. Math. Phys. 19, 1156 (1978) CrossRef
P.J. Olver, Applications of Lie groups to differential equations (Springer-Verlag, NY, 2000)
B. Fornberg, A practical guide to pseudospectral methods (Cambridge University Press, UK, 1998)
Lax, P.D., Richtmyer, R.D., Commun. Pure Appl. Math. 9, 267 (1956) CrossRef