Asymptotics of perturbed soliton for Davey--Stewartson II equation

Abstract

It is shown that, under a small perturbation of lump (soliton) for Davey--Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis shows that, in spite of dispertion, the principal term of the asymptotic expansion for the solution has the solitary wave form up to large time.