Nonlocal Reductions of The Multicomponent Nonlinear Schrödinger Equation on Symmetric Spaces

G. G. Grahovski, J. I. Mustafa, H. Susanto

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Our aim is to develop the inverse scattering transform for multicomponent generalizations of nonlocal reductions of the nonlinear Schrödinger (NLS) equation with PT symmetry related to symmetric spaces. This includes the spectral properties of the associated Lax operator, the Jost function, the scattering matrix, the minimum set of scattering data, and the fundamental analytic solutions. As main examples, we use theManakov vector Schrödinger equation (related to A.III-symmetric spaces) and the multicomponent NLS (MNLS) equations of Kulish–Sklyanin type (related to BD.I-symmetric spaces). Furthermore, we obtain one- and two-soliton solutions using an appropriate modification of the Zakharov–Shabat dressing method. We show that the MNLS equations of these types admit both regular and singular soliton configurations. Finally, we present different examples of one- and two-soliton solutions for both types of models, subject to different reductions.

Original languageBritish English
Pages (from-to)1430-1450
Number of pages21
JournalTheoretical and Mathematical Physics(Russian Federation)
Issue number1
StatePublished - 1 Oct 2018


  • dressing method
  • integrable system
  • inverse scattering transform
  • Lax representation
  • multicomponent nonlinear Schrödinger equation
  • PT symmetry
  • Riemann–Hilbert problem
  • spectral decompositions
  • Zakharov–Shabat system


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