Stability of multi-parameter solitons: asymptotic approach

A general asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems has been developed. The presented approach gives an analytical criterion for oscillatory instability and also predicts novel stationary instability of solitons. Higher order approximations allow one to calculate corresponding eigenvalues with an arbitrary accuracy. It is also shown that asymptotic study of the soliton stability reduces 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 is just the first in the series.