Multisoliton formulas for the multi-component Fokas-Lenells equation with nonzero boundary conditions

TL;DR

This paper derives explicit multisoliton solutions for the multi-component Fokas-Lenells equation under various boundary conditions, using a direct method to obtain compact determinantal formulas.

Contribution

It introduces new multisoliton formulas for the multi-component Fokas-Lenells equation with nonzero boundary conditions, expanding solution methods for this integrable system.

Findings

Multisoliton solutions expressed as compact determinants.

Solutions applicable to both plane-wave and mixed boundary conditions.

Explicit formulas facilitate further analytical and numerical studies.

Abstract

The multi-component Fokas-Lenells equation is considered. In particular, we present the multisoliton formulas for the system with plane-wave boundary conditions, as well as with mixed zero and plane-wave boundary conditions. A direct approach is employed to construct solutions, showing that for both boundary conditions, the multisoliton solutions have compact determinantal expressions.