Type: Article

Higher-order nonlinear Schrödinger equation in 2D case

Hayashi, Nakao; Naumkin, Pavel I.;

Abstract:

We consider the Cauchy problem for the higher-order nonlinear Schrodinger equation in two dimensional case {i partial derivative(t)u( + )b/2 Delta u- 1/4 Delta(2)u = lambda vertical bar u vertical bar u, t > 0,x is an element of R(2. )u( 0 - x) = u0 (x), x is an element of R-2, where lambda is an element of R, b > 0. We develop the factorization techniques for studying the large time asymptotics of solutions to the above Cauchy problem. We prove that the asymptotics has a modified character.