Perturbation of soliton for Davey–Stewartson II equation

It is known that, under a small perturbation (of order $\varepsilon$) of lump (soliton) for Davey–Stewartson (DS-II) equation, the scattering data become nonsoliton. As a result, the solution has the form of Fourier type integral. Asymptotical analysis, given in this work, shows that in spite of dispersion, the main term of the asymptotic expansion for the solution has the solitary wave form up to large time (of order $\varepsilon^{-1}$).