# A nonlocal nonlinear Schrodinger equation derived from a two-layer fluid model

## TL;DR

This paper derives a nonlocal nonlinear Schrödinger equation from a two-layer fluid model, explores its solutions including solitons and kinks, and analyzes its symmetries and reductions.

## Contribution

It introduces a novel nonlocal Schrödinger equation with shifted parity, charge conjugation, and delayed time reversal derived from a fluid model, and studies its solutions and symmetries.

## Key findings

- Obtained elliptic periodic wave solutions including solitons and kinks.
- Derived Lie symmetry group and symmetry reduction solutions for the NNLS equation.
- Provided detailed analysis and figures of the solutions.

## Abstract

By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then a general form of nonlocal nonlinear Schrodinger (NNLS) equation with shifted parity, charge-conjugate and delayed time reversal is obtained by using multi-scale expansion method. Some kinds of elliptic periodic wave solutions of the NNLS equation are obtained by using function expansion method, which contain soliton solutions and kink solutions when the modulus taking as unity. Some representative figures of these solutions are given and analyzed in detail. In addition, by carrying out the classical symmetry method on the NNLS equation, not only the Lie symmetry group but also the related symmetry reduction solutions are given.