New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

P. S. Vinayagam, R. Radha, U. Al Khawaja, Liming Ling

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We investigate generalized nonlocal coupled nonlinear Schorödinger equation containing Self-Phase Modulation, Cross-Phase Modulation and four wave mixing involving nonlocal interaction. By means of Darboux transformation we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soltion interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of four wave mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of four wave mixing results in the generation of a new solutions which is spatially and temporally periodic called “Soliton (Breather) lattice”.

Original languageEnglish
Pages (from-to)387-395
Number of pages9
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume59
DOIs
Publication statusPublished - Jun 2018

Keywords

  • Breathers
  • Coupled nonlinear Schrödinger system
  • Darboux transformation
  • Four-wave mixing
  • Lax pair
  • Soliton

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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