arXiv subjects
Publications and source records attributed to R. R. Gadyl'shin.
We obtain necessary and sufficient conditions for emerging of small eigenvalue for Schrödinger operator on plane under local operator perturbations. In the case the eigenvalue emerges we construct its asymptotics. The examples are given.
We adduce the necessary and sufficient condition for arising of eigenvalues of Shrodinger operator in axis under small local perturbations. In the case of eigenvalues arising we construct their asymptotics.
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.
We show that lumps (solitons) of the Davey--Stewartson II equation fail under small perturbations of initial data.