Localized Solitons of a (2+1)-dimensional Nonlocal Nonlinear Schr\"odinger Equation

TL;DR

This paper introduces a new integrable (2+1)-dimensional nonlocal nonlinear Schrödinger equation, providing explicit N-soliton solutions and analyzing their unique interaction behaviors, including amplitude changes after collisions.

Contribution

It presents a novel integrable nonlocal nonlinear Schrödinger equation in (2+1) dimensions with explicit Gram determinant solutions and studies their interaction dynamics.

Findings

Localized N-soliton solutions exhibit amplitude changes after collisions.

The solutions are expressed via Gram type determinants.

The equation is shown to be integrable.

Abstract

A new integrable (2+1)-dimensional nonlocal nonlinear Schr\"odinger equation is proposed. The $N$-soliton solution is given by Gram type determinant. It is found that the localized N-soliton solution has interesting interaction behavior which shows change of amplitude of localized pulses after collisions.