Type: Article

Scattering of solutions to the fourth order nonlinear Schrödinger equation

Hayashi, Nakao; Méndez Navarro, Jesús A, Naumkin, Pavel I.;

Abstract:

We consider the Cauchy problem for the fourth-order nonlinear Schrodinger equation {i partial derivative(t) u + 1/4 partial derivative(4)(x) u = lambda vertical bar u vertical bar (rho-1) u, t > 0, x is an element of R, n(0, x) = u(0) (x), x is an element of R, where lambda is an element of C, rho > 4. We introduce the factorization for the free evolution group to prove the large time asymptotics of solutions.