English

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Exactly Solvable and Integrable Systems 2024-02-13 v1

Abstract

We propose the Hirota bilinearization of the Fokas-Lenells derivative nonlinear Schrodinger equation with a non-vanishing background. The bilinear method is applied using an auxilary function to obtain the dark one soliton solution, dark two soliton solution and eventually the scheme for obtaining dark N soliton solutions. The use of auxilary function in bilinearization makes the method simpler than the ones reported earlier. Later, we have introduced a Lax pair for this integrable equation and using a transformation we have shown that this system is gauge equivalent to a spin system, namely the Landau-Lifshitz equation.

Keywords

Cite

@article{arxiv.2307.15136,
  title  = {Fokas-Lenells equation dark soliton and gauge equivalent spin equation},
  author = {Riki Dutta and Sagardeep Talukdar and Gautam Kumar Saharia and Sudipta Nandy},
  journal= {arXiv preprint arXiv:2307.15136},
  year   = {2024}
}