Integrability and multisoliton solutions of the reverse space and/or time nonlocal Fokas–Lenells equation

Abstract

This paper studies reverse space and/or time nonlocal Fokas–Lenells (FL) equation, which describes the propagation of nonlinear light pulses in monomode optical fibers when certain higher-order nonlinear effects are considered, by Hirota bilinear method. Firstly, we construct variable transformations from reverse space nonlocal FL equation to reverse time and reverse space-time nonlocal FL equations. Secondly, the multisoliton and quasi-periodic solutions of the reverse space nonlocal FL equation are derived through Hirota bilinear method, and the soliton solutions of reverse time and reverse space-time nonlocal FL equations are given through variable transformations. Also, dynamical behaviors of the multisoliton solutions are discussed in detail by analyzing their wave structures. Thirdly, asymptotic analysis of two- and three-soliton solutions of reverse space nonlocal FL equation is used to investigate the elastic interaction and inelastic interaction. Finally, the infinite conservation laws of three types of nonlocal FL equations are found by using their lax pairs. The results obtained in this paper possess new properties that different from the ones for FL equation, which are useful in exploring novel physical phenomena of nonlocal systems in nonlinear media.