Mixed soliton solutions of the defocusing nonlocal nonlinear Schrodinger equation

TL;DR

This paper constructs new mixed soliton solutions for the defocusing nonlocal nonlinear Schrödinger equation using Darboux transformation, revealing complex interactions with unique velocity and phase shift behaviors.

Contribution

It introduces two novel types of mixed soliton solutions and analyzes their elastic interactions and asymptotic behaviors, including degenerate cases.

Findings

First type exhibits elastic interactions with dark and antidark solitons.

Second type shows four-soliton interactions with t-dependent velocities.

Asymptotic analysis reveals phase shifts grow logarithmically with |t|.

Abstract

By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrodinger 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 technique, 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 asymptotic mixed 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.