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