Mixed soliton solutions of the defocusing nonlocal nonlinear Schrödinger equation

Abstract

By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrödinger equation. We reveal that the first type of solution can display a large variety of interactions among two exponential solitons and two rational solitons, in which the standard elastic interaction properties are preserved and each soliton could be either the dark or antidark type. By developing the asymptotic analysis method, we also find that the second type of solution can exhibit the elastic interactions among four mixed asymptotic solitons. But in sharp contrast to the common solitons, the mixed asymptotic solitons have the t-dependent velocities and their phase shifts before and after interaction also grow with |t| in the logarithmical manner. In addition, we discuss the degenerate cases for such two types of mixed soliton solutions when the four-soliton interaction reduces to a three-soliton or two-soliton interaction.