Integrability and Multisoliton Solutions of the Reverse Space or/and Time Nonlocal Fokas-Lenells (FL) Equation

Abstract

This paper studies reverse space or/and 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, variable transformations from reverse space nonlocal FL equation to reverse time and reverse space-time nonlocal FL equations are constructed. Secondly, the one-, two- and three-soliton 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. 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 investigated the elastic interaction and inelastic interaction. At last, the Lax integrability and conservation laws of three types of nonlocal FL equations is studied. 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.

Mixed localized wave solutions of the (2+1)-dimensional Fokas-Lenells equation

“…The generalization of FL equation has also been researched, such as multi-component [13], nonlocal [14] as well as (2+1)-dimensional FL equations [15][16][17]. Recently, we proposed the following (2+1)-dimensional FL equation with parameters iq xt − iαq xx − iq xy + 2γq x − 4βq x qq * + 4iβq = 0, (1.1) and investigated the conservation law, modulation instability and higher-order rogue wave solutions [15].…”