Lattice representation and dark solitons of the Fokas-Lenells equation

TL;DR

This paper explores the Fokas-Lenells equation, an integrable generalization of the nonlinear Schrödinger equation, analyzing its lattice structure, relationships with other models, and deriving multi-dark soliton solutions.

Contribution

It introduces the lattice representation of the Fokas-Lenells equation and derives explicit N-dark soliton solutions through reductions to known integrable models.

Findings

Established the connection between Fokas-Lenells and other integrable equations.

Derived explicit N-dark soliton solutions.

Provided insights into the equation's lattice structure.

Abstract

This work is devoted to an integrable generalization of the nonlinear Schr\"odinger equation proposed by Fokas and Lenells. I discuss the relationships between this equation and other integrable models. Using the reduction of the Fokas-Lenells equation to the already known ones I obtain the N-dark soliton solutions.