Stability of Solitary Waves for a Generalized Nonlinear Coupled Schrodinger Systems

Abstract

In this paper we show that the standing waves of the form(

ei tu(x), ei tu(x)), > 0, u(x) real and positive, are stable for the system i@u@t +uxx+ (|u|2p−2 + |v|p|u|p−2)u = 0 @v@t+vxx+(|u|p|v|p−2 + |v|2p−2)v = 0 provided 2 p < 3 and 0 < 6= p − 1. The Morse index of such solution is one for > p − 1 and two for 0< y< p − 1 but it is stable in both cases.