Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities

Abstract

AbstractThis paper proves existence and stability of solitary-wave solutions of a system of 2-coupled nonlinear Schrödinger equations with power-type nonlinearities arising in several models of modern physics. The existence of vector solitary-wave solutions (i.e., both components are nonzero) is established via variational methods. The set of minimizers is shown to be stable and further information about the structures of this set are given. The results extend stability results previously obtained by Cipolatti and Zumpichiatti [Nonlinear Anal. 42 (2000), 445–461], Nguyen and Wang [Adv. Differential Equations 16 (2011), no. 9–10, 977–1000; `Existence and stability of a two-parameter family of solitary waves for a 2-coupled nonlinear Schrödinger system', preprint (2013)], and Ohta [Nonlinear Anal. 26 (1996), 933–939].