Orbital stability of solitary waves for a nonlinear Schrödinger system

Abstract

In this paper, we study the coupled nonlinear Schrödinger system where u; v are complex-valued functions of (x, t) ε R2, and a; b; c 2 ℝ. Our work shows that, for this system of equations, the interplay between components of solutions in terms of the parameters a; b; c plays an important role in both the existence and stability of solitary waves. In particular, we prove that solitary wave solutions to this system are orbitally stable when either 0 < b < min{a,c}, or b > 0 with b > maxfa; cg and b2 > ac.