Integrable Nonlocal Nonlinear Schrödinger Equation

TLDR

A new integrable nonlocal nonlinear Schrödinger equation is introduced. The authors introduce a new integrable nonlocal nonlinear Schrödinger equation, analyze it via the inverse scattering transform with symmetric scattering data, and present a method for constructing pure soliton solutions. The equation has a Lax pair, infinite conservation laws, PT symmetry, and admits an explicit breathing one‑soliton solution whose key properties are contrasted with the classical nonlinear Schrödinger equation.

Abstract

A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and scattering data with suitable symmetries are discussed. A method to find pure soliton solutions is given. An explicit breathing one soliton solution is found. Key properties are discussed and contrasted with the classical nonlinear Schrödinger equation.