Dynamics of discrete soliton propagation and elastic interaction in a higher-order coupled Ablowitz-Ladik equation

Abstract Under investigation is a higher-order coupled Ablowitz–Ladik equation whose integrability is established in the sense of Lax pair. With symbolic computation, the N -fold Darboux transformation is used to construct discrete multi-soliton solutions in the determinant form. Soliton propagation and elastic interaction features are investigated through asymptotic analysis and analyzing some important physical quantities. Numerical simulations are used to explore the dynamical stability of one- and two-soliton solutions.

[1]  Tao Xu,et al.  Darboux transformation and analytic solutions of the discrete PT-symmetric nonlocal nonlinear Schrödinger equation , 2016, Appl. Math. Lett..

[2]  Wen-Xiu Ma,et al.  Complexiton solutions of the Toda lattice equation , 2004 .

[3]  Mark J. Ablowitz,et al.  Nonlinear differential−difference equations , 1975 .

[4]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[5]  Long Lee,et al.  The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schr\"odinger equation , 2012, 1207.0824.

[6]  Xiaoyong Wen,et al.  Modulational instability and higher order-rogue wave solutions for the generalized discrete Hirota equation , 2018, Wave Motion.

[7]  Bo Tian,et al.  Rogue waves for the coupled variable-coefficient fourth-order nonlinear Schrödinger equations in an inhomogeneous optical fiber , 2018 .

[8]  Bo Tian,et al.  Mixed lump-kink and rogue wave-kink solutions for a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics , 2018 .

[9]  Fajun Yu,et al.  Explicit solution and Darboux transformation for a new discrete integrable soliton hierarchy with 4×4 Lax pairs , 2017 .

[10]  Bo Tian,et al.  Solitons for the (2+1)-dimensional Konopelchenko–Dubrovsky equations , 2018 .

[11]  Da-Wei Zuo,et al.  Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation , 2016 .

[12]  Morikazu Toda,et al.  Theory Of Nonlinear Lattices , 1981 .

[13]  Bao-Feng Feng,et al.  Rational solutions to two- and one-dimensional multicomponent Yajima–Oikawa systems , 2015 .

[14]  Da-Wei Zuo,et al.  Dynamics of the optical solitons for a (2+1)-dimensional nonlinear Schrödinger equation , 2017 .

[15]  Da-Wei Zuo,et al.  Modulation instability and breathers synchronization of the nonlinear Schrödinger Maxwell-Bloch equation , 2018, Appl. Math. Lett..

[16]  Bo Tian,et al.  Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev–Petviashvili equation in fluid mechanics , 2019, Chinese Journal of Physics.

[17]  Gui-Fang Zhang,et al.  Exact solutions of the nonlocal Hirota equations , 2019, Appl. Math. Lett..

[18]  Da-Wei Zuo,et al.  Interaction of the nonautonomous soliton in the optical fiber , 2016 .

[19]  Xiao-Yong Wen,et al.  N-fold Darboux transformation and explicit solutions in terms of the determinant for the three-field Blaszak-Marciniak lattice , 2013, Appl. Math. Lett..

[20]  Xianguo Geng,et al.  Nonlinearization of the Lax pairs for discrete Ablowitz–Ladik hierarchy , 2007 .

[21]  Yasuhiro Ohta,et al.  General rogue waves in the focusing and defocusing Ablowitz–Ladik equations , 2014 .

[22]  Bo Tian,et al.  Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional Davey-Stewartson system on surface waves of finite depth , 2018 .

[23]  Bo Tian,et al.  Conservation laws, binary Darboux transformations and solitons for a higher-order nonlinear Schrödinger system , 2019, Chaos, Solitons & Fractals.

[24]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[25]  Hui-Qin Hao,et al.  N-fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation , 2018, Appl. Math. Lett..

[26]  Wenxiu Ma,et al.  Rational solutions of the Toda lattice equation in Casoratian form , 2004 .

[27]  Abdul-Majid Wazwaz,et al.  Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations , 2019, Appl. Math. Lett..

[28]  Yi-Tian Gao,et al.  Multi-soliton solutions for the three-coupled KdV equations engendered by the Neumann system , 2014 .

[29]  Xiaoyong Wen.  Elastic Interaction and Conservation Laws for the Nonlinear Self-Dual Network Equation in Electric Circuit , 2012 .

[30]  Li-Yuan Ma,et al.  N-soliton solution for an integrable nonlocal discrete focusing nonlinear Schrödinger equation , 2016, Appl. Math. Lett..

[31]  Bo Tian,et al.  Rogue waves and solitons of the coherently-coupled nonlinear Schrödinger equations with the positive coherent coupling , 2018, Physica Scripta.

[32]  Xin-Yi Gao,et al.  Looking at a nonlinear inhomogeneous optical fiber through the generalized higher-order variable-coefficient Hirota equation , 2017, Appl. Math. Lett..

[33]  M. Wadati,et al.  Transformation Theories for Nonlinear Discrete Systems , 1976 .

[34]  Tao Xu,et al.  Generation mechanism of rogue waves for the discrete nonlinear Schrödinger equation , 2018, Appl. Math. Lett..

[35]  V. Matveev,et al.  Darboux Transformations and Solitons , 1992 .

[36]  Bo Tian,et al.  Lie group analysis, analytic solutions and conservation laws of the (3 + 1)-dimensional Zakharov-Kuznetsov-Burgers equation in a collisionless magnetized electron-positron-ion plasma , 2018, The European Physical Journal Plus.

[37]  B. Malomed,et al.  Solitary waves with damped oscillatory tails: an analysis of the fifth-order Korteweg-de Vries equation , 1994 .

[38]  Xin-Yi Gao,et al.  Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas , 2019, Appl. Math. Lett..