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Theoretical and Mathematical Physics

, Volume 196, Issue 3, pp 1241–1267 | Cite as

Inverse Scattering Transform for the Nonlocal Reverse Space–Time Nonlinear Schrödinger Equation

  • M. J. Ablowitz
  • Bao-Feng Feng
  • Xu-Dan Luo
  • Z. H. Musslimani
Article

Abstract

Nonlocal reverse space–time equations of the nonlinear Schrödinger (NLS) type were recently introduced. They were shown to be integrable infinite-dimensional dynamical systems, and the inverse scattering transform (IST) for rapidly decaying initial conditions was constructed. Here, we present the IST for the reverse space–time NLS equation with nonzero boundary conditions (NZBCs) at infinity. The NZBC problem is more complicated because the branching structure of the associated linear eigenfunctions is complicated. We analyze two cases, which correspond to two different values of the phase at infinity. We discuss special soliton solutions and find explicit one-soliton and two-soliton solutions. We also consider spatially dependent boundary conditions.

Keywords

inverse scattering transform nonlocal RST NLS equation 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • M. J. Ablowitz
    • 1
  • Bao-Feng Feng
    • 2
  • Xu-Dan Luo
    • 3
  • Z. H. Musslimani
    • 4
  1. 1.Department of Applied MathematicsUniversity of Colorado at BoulderBoulderUSA
  2. 2.School of Mathematical and Statistical SciencesUniversity of Texas Rio Grande ValleyEdinburgUSA
  3. 3.Department of MathematicsState University of New York at BuffaloBuffalo, New YorkUSA
  4. 4.Department of MathematicsFlorida State UniversityTallahasseeUSA

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