A note on decay rates of solutions to a system of cubic nonlinear Schrödinger equations in one space dimension

Abstract

We consider the initial value problem for a system of cubic nonlinear Schrödinger equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution exists globally and decays of the rate $O(t^{-1/2}(\log t{)}^{-1/2})$ in $L^{\infty }$ as $t$ tends to infinity, if the system satisfies certain mass relations.

12 pages

References in corpus (2)

• Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
• Global existence of small amplitude solutions to one-dimensional nonlinear Klein-Gordon systems with different masses

Cited by in corpus (4)

• Large time asymptotics for a cubic nonlinear Schrödinger system in one space dimension
• On Agemi-type structural conditions for a system of semilinear wave equations
• Large time asymptotics for a cubic nonlinear Schrödinger system in one space dimension, II
• On the derivative nonlinear Schrödinger equation with weakly dissipative structure