Structural transformation of eigenvalues for a perturbed algebraic soliton potential

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 structural 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.