Integrable Nonlocal Nonlinear Schr\"odinger Equation

Integrable Nonlocal Nonlinear Schrödinger Equation

Mark J. Ablowitz and Ziad H. Musslimani

Phys. Rev. Lett. 110, 064105 – Published 7 February 2013

Abstract

A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is $P T$ 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.

Received 22 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.064105

Authors & Affiliations

Mark J. Ablowitz¹ and Ziad H. Musslimani²

¹Department of Applied Mathematics, University of Colorado, Campus Box 526, Boulder, Colorado 80309-0526
²Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510