Spin system equivalent to the integrable Fokas-Lenells equation

Abstract

It is well known that integrable nonlinear Schodinger-type equations, such as the classical nonlinear Schodinger
equation, the nonlinear Schodinger equation of the derived type, play an important role in the study of wave propagation. Recently, a new integrable model, called the Fokas-Lenells equation (FL), was proposed in mono-model optical fibers. It is interesting that unlike the nonlinear Schodinger equation, the FL equation admits both bright and dark soliton solutions without changing the sign of the nonlinear term. Bright soliton solutions were constructed using the Hirota bilinear method, and dark soliton solutions were constructed by the Hirota bilinear method and the Bekllund transformation. Thus, using the well-known
transformation methods, we can find various soliton solutions of the FL equation. For this, it is necessary to carefully analyze the FL equation. In this paper we find a spin system that is gauge-equivalent to the (1 + 1) -dimensional integrable Fokas-Lenells equation. The Lax representation for this system is obtained. The result obtained can be used for further investigation of spin
systems.