Type: Article

Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case

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(4)u, (t,x) is an element of R+ x R, u(0,x) = u(0) (x) , x is an element of R. We prove the large time asymptotic behavior of solutions with a logarithmic correction under the conditions integral u(0) (x)dx not equal 0, lambda > 0