English

The Fokas-Lenells equations: Bilinear approach

Exactly Solvable and Integrable Systems 2021-10-01 v3

Abstract

In this paper, the Fokas-Lenells equations are investigated via bilinear approach. We bilinearize the unreduced Fokas-Lenells system, derive double Wronskian solutions, and then, by means of a reduction technique we obtain variety of solutions of the reduced equations. This enables us to have a full profile of solutions of the classical and nonlocal Fokas-Lenells equations. Some obtained solutions are illustrated based on asymptotic analysis. As a notable new result, we obtain solutions to the Fokas-Lenells equation, which are related to real discrete eigenvalues and not reported before in the analytic approaches. These solutions behave like (multi-)periodic waves or solitary waves with algebraic decay. In addition, we also obtain solutions to the two-dimensional massive Thirring model from those of the Fokas-Lenells equation.

Keywords

Cite

@article{arxiv.2104.04938,
  title  = {The Fokas-Lenells equations: Bilinear approach},
  author = {Shu-zhi Liu and Jing Wang and Da-jun Zhang},
  journal= {arXiv preprint arXiv:2104.04938},
  year   = {2021}
}

Comments

32 pages, 11 figures, appendixes and references updated

R2 v1 2026-06-24T01:02:53.697Z