Type: Article

KDV type asymptotics for solutions to higher-order nonlinear-Schrödinger equations

Naumkin, Pavel I; Sánchez-Suárez, Isahí;

Abstract:

We consider the Cauchy problem for the higher-order nonlinear Schrodinger equation i partial derivative(t)u - a/3 vertical bar partial derivative(x)vertical bar(3)u - b/4 partial derivative(4)(x)u = lambda i partial derivative(x) (vertical bar u vertical bar(2)u), (t, x) is an element of R+ x R, u(0, x) = u(0)(x), x is an element of R, where a, b > 0, vertical bar partial derivative(x)vertical bar(alpha) = F-1 vertical bar xi vertical bar F-alpha and F is the Fourier transformation. Our purpose is to study the large time behavior of the solutions under the non-zero mass condition integral u(0)(x)dx not equal 0.