D.E. Pelinovsky and R.H.J. Grimshaw

Structural transformation of eigenvalues for a perturbed algebraic soliton potential

Physics Letters A 229, 165-172 (1997)

Abstract:
We present a modified perturbation technique for the AKNS spectral system to evaluate eigenvalues supported by a perturbed algebraic soliton potential. The results of this technique are applied to the problem of the structral instability of algebraic solitons in the modified Korteweg-de Vries equation. It is shown analytically and numerically that the algebraic soliton is destroyed under the action of small initial perturbations and transforms either to a steady-state soliton with exponentially decaying tails or to a pulsating ''breather''-type wave packet.

Keywords:
NONLINEAR SCHRODINGER EQUATION, SCATTERING TRANSFORM, INSTABILITIES, WAVES