Existence of Generalized Heteroclinic Solutions of the Coupled Schrdinger System under a Small Perturbation

The following coupled Schrdinger system with a small perturbation uxx + u- u3+ βuv2+ f(, u, ux, v, vx) = 0 in R,vxx- v + v3+ βu2v + g(, u, ux, v, vx) = 0 in R is considered, where β and are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution(called the generalized heteroclinic solution thereafter).