Inverse scattering transform and the soliton solution of the discrete Ablowitz-Ladik equation

被引：0
|
作者：
Li, Yin [1 ]
Chen, Meisen [2 ]
机构：
[1] Shaoguan Univ, Sch Math & Stat, Shaoguan 512005, Peoples R China
[2] Fujian Normal Univ, Sch Math & Stat, Fuzhou 350117, Peoples R China
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2025年 / 472卷
基金：
中国国家自然科学基金;
关键词：
Discrete Ablowitz-Ladik equation; Inverse scattering transform; Multiple-pole solution; Riemann-Hilbert method; LONG-TIME ASYMPTOTICS; TODA LATTICE; INTEGRABILITY;
D O I：
10.1016/j.physd.2024.134517
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper studies the discrete Ablowitz-Ladik equation via the Riemann-Hilbert (RH) approach. By its matrix spectral problem and Lax pair, the Jost solution and the reflection coefficients are constructed. Based on the zero curvature formulation, we assume that there are higher-order zeros for the scattering coefficient a(A), and construct the corresponding RH problem. The inverse scattering transform of the discrete Ablowitz-Ladik equation is presented by the matrix spectral problem, the reconstruction formula and the RH problem, which enables us to obtain the multiple-pole solutions. And then the dynamics of one-and two-soliton solutions are discussed and presented graphically. Compared with simple-pole solutions, multiple-pole solutions possess more complicated profiles.
引用
收藏
页数：7
相关论文
共 50 条
  • [1] Dark soliton collisions of a discrete Ablowitz-Ladik equation for an electrical/optical system
    Xie, Xi-Yang
    Tian, Bo
    Wu, Xiao-Yu
    Jiang, Yan
    OPTICAL ENGINEERING, 2016, 55 (10)
  • [2] Soliton collisions of a discrete Ablowitz-Ladik equation with variable coefficients for an electrical/optical system
    Xie, Xi-Yang
    Tian, Bo
    Chai, Jun
    Wu, Xiao-Yu
    Jiang, Yan
    OPTICAL AND QUANTUM ELECTRONICS, 2017, 49 (04)
  • [3] Discrete bright-dark soliton solutions and parameters controlling for the coupled Ablowitz-Ladik equation
    Li, Li
    Yu, Fajun
    NONLINEAR DYNAMICS, 2017, 89 (04) : 2403 - 2414
  • [4] Nonlocal Reductions of the Ablowitz-Ladik Equation
    Grahovski, G. G.
    Mohammed, A. J.
    Susanto, H.
    THEORETICAL AND MATHEMATICAL PHYSICS, 2018, 197 (01) : 1412 - 1429
  • [5] l 2-Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systems
    Chen, Meisen
    Fan, Engui
    He, Jingsong
    PHYSICA D-NONLINEAR PHENOMENA, 2023, 443
  • [6] On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude
    Boadi, E. C.
    Charalampidis, E. G.
    Kevrekidis, P. G.
    Ossi, N. J.
    Prinari, B.
    WAVE MOTION, 2025, 134
  • [7] Multi-Hamiltonian Structure for the Finite Defocusing Ablowitz-Ladik Equation
    Gekhtman, Michael
    Nenciu, Irina
    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (02) : 147 - 182
  • [8] Optical discrete rogue wave solutions and numerical simulation for a coupled Ablowitz-Ladik equation with variable coefficients
    Li, Li
    Yu, Fajun
    NONLINEAR DYNAMICS, 2018, 91 (03) : 1993 - 2005
  • [9] Symmetries for the Ablowitz-Ladik Hierarchy: Part II. Integrable Discrete Nonlinear Schrodinger Equations and Discrete AKNS Hierarchy
    Zhang, Da-Jun
    Chen, Shou-Ting
    STUDIES IN APPLIED MATHEMATICS, 2010, 125 (04) : 419 - 443
  • [10] INVERSE SCATTERING TRANSFORM AND SOLITON SOLUTIONS OF AN INTEGRABLE NONLOCAL HIROTA EQUATION
    Li, Yuan
    Tian, Shou-Fu
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2022, 21 (01) : 293 - 313
12345