Stability of multi-parameter solitons: Asymptotic approach

Abstract

General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=δH/δE_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability can be reduced to the calculation of a certain sequence of the determinants, where the famous determinant of the matrix consisting from the derivatives of the system invariants with respect to the soliton parameters is just the first in the series. The presented approach gives first analytical criterion for the oscillatory instability and also predicts novel stationary instability. Higher order approximations allow to calculate corresponding eigenvalues with arbitrary accuracy.