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.

This paper focuses on the exact soliton solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito equations with time-dependent linear phase speed. Based on the Painlevé integrability test of this equation, the condition of the integrability is determined. Then the general N-soliton solutions are constructed by Hirota bilinear method. Not only the expressions of exact solutions and their degenerations, but also the spatial structures are presented for different choices of the parameters, including the line soliton, periodic soliton, lump soliton and their interaction forms.

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In this paper, the reverse space-time nonlocal Sasa-Satsuma equation is introduced from the coupled Sasa-Satsuma system via the specific solution constraint. Soliton and multisolitons solutions of the reverse spacetime nonlocal Sasa-Satsuma equation are derived through the following steps: 1) The inverse scattering transform method of the coupled Sasa-Satsuma system is carried out, and then the solutions for the system are obtained through solving the established Riemann-Hilbert problems; 2) The symmetry relations of discrete eigenvalues and eigenvectors for the reverse space-time nonlocal Sasa-Satsuma equation are analyzed under the specific solution constraint; 3) Based on the symmetry constraints, the one-soliton and two-soliton solutions are derived, and their dynamics is investigated. Finally, asymptotic analysis of two-soliton solutions for the reverse space-time nonlocal Sasa-Satsuma equation is used to study. The results shown some interesting physical feature and mathematical properties, which might be useful to comprehend nonlocal nonlinear system.