Large time asymptotics for a cubic nonlinear Schrödinger system in one space dimension

Abstract

We consider a two-component system of cubic nonlinear Schrödinger equations in one space dimension. We show that each component of the solutions to this system behaves like a free solution in the large time, but there is a strong restriction between the profiles of them. This turns out to be a consequence of non-trivial long-range nonlinear interactions.

16 pages

References in corpus (1)

• On Agemi-type structural conditions for a system of semilinear wave equations

Cited by in corpus (2)

• Energy decay for small solutions to semilinear wave equations with weakly dissipative structure
• Non-decay of the energy for a system of semilinear wave equations