Approximate analytical description for the nonlinear   -symmetric coupled-mode equations

In this paper, we present an approximate analytical description of the solutions dynamics of nonlinear   -symmetric coupled-mode equations which can be used to realize the nonlinear   -symmetric optical configuration. By the multiple-scale analysis, we construct the asymptotic solutions of the coupled-mode equations. In the   -symmetry unbroken region, there is a good agreement between the asymptotic solutions and exact numerical solutions, and the higher-order asymptotic series can yield a higher accuracy. However, in the   -symmetry broken region, the asymptotic solutions become invalid quickly as z increases. Instead, we neglect one linear coupling term and obtain the approximate analytical solutions which, to some extent, describe the dynamics in the   -symmetry broken region when z ≫ 1. This paper may be helpful for undergraduate and graduate students in physics to understand the nonlinear dynamics of   -symmetric systems.