Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, N-fold Darboux transformation and explicit exact solutions

Yuan Shen, Bo Tian, Tian-Yu Zhou and Xiao-Tian Gao

Chaos, Solitons & Fractals, 2022, vol. 164, issue C

Abstract: Nonlinear differential-difference equations appear in optics, condensed matter physics, plasma physics and other fields. In this paper, we investigate a nonlinear differential-difference hierarchy relevant, in the case of θ=0, to the Ablowitz-Ladik equation, where θ=0,1. That hierarchy is obtained via a discrete spectral problem and the associated discrete spectral problem. When θ=1, Lax pair of the first nonlinear differential-difference system in that hierarchy is obtained. When θ=1, conservation laws and N-fold Darboux transformation of the first nonlinear differential-difference system in that hierarchy are derived with the aid of that Lax pair, where N is a positive integer. When θ=1, explicit exact solutions of that system are determined via that N-fold Darboux transformation. Discrete one soliton and interaction between the discrete one soliton and one breather-like wave are graphically depicted.

Keywords: Nonlinear differential-difference hierarchy; Lax pair; Conservation laws; N-fold Darboux transformation; Explicit exact solutions (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922006701

DOI: 10.1016/j.chaos.2022.112460

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