Soliton management for a variable-coefficient modified Korteweg–de Vries equation
- 5 August 2011
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 84 (2), 026606
- https://doi.org/10.1103/physreve.84.026606
Abstract
The concept of soliton management has been explored in the Bose-Einstein condensate and optical fibers. In this paper, our purpose is to investigate whether a similar concept exists for a variable-coefficient modified Korteweg–de Vries equation, which arises in the interfacial waves in two-layer liquid and Alfvén waves in a collisionless plasma. Through the Painlevé test, a generalized integrable form of such an equation has been constructed under the Painlevé constraints of the variable coefficients based on the symbolic computation. By virtue of the Ablowitz-Kaup-Newell-Segur system, a Lax pair with time-dependent nonisospectral flow of the integrable form has been established under the Lax constraints which appear to be more rigid than the Painlevé ones. Under such Lax constraints, multisoliton solutions for the completely integrable variable-coefficient modified Korteweg–de Vries equation have been derived via the Hirota bilinear method. Moreover, results show that the solitons and breathers with desired amplitude and width can be derived via the different choices of the variable coefficients. DOI: http://dx.doi.org/10.1103/PhysRevE.84.026606 ©2011 American Physical SocietyKeywords
This publication has 43 references indexed in Scilit:
- Inelastic interactions of the multiple-front waves for the modified Kadomtsev–Petviashvili equation in fluid dynamics, plasma physics and electrodynamicsWave Motion, 2009
- Breather generation in fully nonlinear models of a stratified fluidPhysical Review E, 2007
- New exact solutions to the mKdV equation with variable coefficientsChaos, Solitons, and Fractals, 2006
- Interactions of breathers and solitons in the extended Korteweg–de Vries equationWave Motion, 2005
- A class of doubly periodic waves for nonlinear evolution equationsWave Motion, 2002
- Dynamics of localized waves with large amplitude in a weakly dispersive medium with a quadratic and positive cubic nonlinearityJournal of Experimental and Theoretical Physics, 2001
- Interactions between polarized soliton pulses in optical fibers: Exact solutionsPhysical Review E, 1996
- Symmetries, conservation laws and Hamiltonian structures of the non-isospectral and variable coefficient KdV and MKdV equationsJournal of Physics A: General Physics, 1995
- Non-propagating solitons of the non-isospectral and variable coefficient modified KdV equationJournal of Physics A: General Physics, 1994
- On interfacial solitary waves over slowly varying topographyJournal of Fluid Mechanics, 1984