Exact solutions of nonlocal Fokas-Lenells equation

Abstract In this paper we propose a nonlocal Fokas–Lenells (FL) equation which can be derived from the Kaup–Newell (KN) linear scattering problem. By constructing the Darboux transformation of nonlocal FL equation, we obtain its different kinds of exact solutions including bright/dark solitons, kink solutions, periodic solutions and several types of mixed soliton solutions. It is shown that the solutions of nonlocal FL equation possess different properties from the normal FL equation.

[1]  M. Ablowitz,et al.  Integrable Nonlocal Nonlinear Equations , 2016, 1610.02594.

[2]  M. Ablowitz,et al.  Integrable nonlocal nonlinear Schrödinger equation. , 2013, Physical review letters.

[3]  General soliton solutions to a coupled Fokas-Lenells equation , 2016, 1611.10057.

[4]  Jinyun Yuan,et al.  Integrable Semi-discrete Kundu–Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory , 2018, J. Nonlinear Sci..

[5]  Zuo-Nong Zhu,et al.  On a nonlocal modified Korteweg-de Vries equation: Integrability, Darboux transformation and soliton solutions , 2017, Commun. Nonlinear Sci. Numer. Simul..

[6]  Yoshimasa Matsuno,et al.  A direct method of solution for the Fokas–Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions , 2012, 1205.3243.

[7]  M. Ablowitz,et al.  Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation , 2016 .

[8]  Jingsong He,et al.  Rogue Waves of the Fokas–Lenells Equation , 2012, 1209.5540.

[9]  S. Lou,et al.  Alice-Bob Physics: Coherent Solutions of Nonlocal KdV Systems , 2016, Scientific Reports.

[10]  A. S. Fokas,et al.  Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation , 2016 .

[11]  Shu-Min Zhang,et al.  Variable sinh-Gaussian solitons in nonlocal nonlinear Schrödinger equation , 2018, Appl. Math. Lett..

[12]  Hai-qiong Zhao.  Integrable nonholonomic deformation of modified Volterra lattice equation , 2019, Appl. Math. Lett..

[13]  Boling Guo,et al.  Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation , 2012 .

[14]  Jingsong He,et al.  The n‐order rogue waves of Fokas–Lenells equation , 2012, 1211.5924.

[15]  A. Fokas.  On a class of physically important integrable equations , 1994 .