articlePhysical Review LettersFeb 7, 2013Closed access

Integrable Nonlocal Nonlinear Schrödinger Equation

MJMark J. AblowitzZHZiad H. Musslimani

University of Colorado Boulder · Florida State University

PubMed
Indexed incrossrefpubmed

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.

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Topics & keywords

Topics
Keywords
  • Integrable system
  • Nonlinear Schrödinger equation
  • Conservation law
  • Inverse scattering transform
  • Soliton
  • Lax pair
  • Physics
  • Homogeneous space
UN Sustainable Development Goals
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