Rational solutions of the defocusing non-local nonlinear Schrödinger equation: asymptotic analysis and soliton interactions

Abstract

In this paper, we obtain the N th-order rational solutions for the defocusing non-local nonlinear Schrödinger equation by the Darboux transformation and some limit technique. Then, via an improved asymptotic analysis method relying on the balance between different algebraic terms, we derive the explicit expressions of all asymptotic solitons of the rational solutions with the order 1 ≤ N ≤ 4 . It turns out that the asymptotic solitons are localized in the straight lines or algebraic curves, and the exact solutions approach the curved asymptotic solitons with a slower rate than the straight ones. Moreover, we find that all the rational solutions exhibit just five different types of soliton interactions, and the interacting solitons are divided into two halves with each having the same amplitudes. Particularly for the curved asymptotic solitons, there may exist a slight difference for their velocities between at t and − t with certain parametric conditions. In addition, we reveal that the soliton interactions in the rational solutions with N ≥ 2 are stronger than those in the exponential and exponential-and-rational solutions.