The focusing coupled nonlinear Schr\"odinger equation with parallel nonzero boundary conditions: long--time asmptotics
We study the long-time behavior of solutions of the focusing coupled nonlinear Schr\"odinger equations with parallel constant nonzero boundary conditions in the solitonless setting. We distinguish three types of asymptotic regions: plane-wave regions, modulated elliptic-wave regions, and Painlev\'e-II transition region...