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SOLUTIONS OF LOCAL AND NONLOCAL DISCRETE COMPLEX MODIFIED KORTEWEG-DE VRIES EQUATIONS AND CONTINUUM LIMITS
  • YA-NAN HU,
  • Shoufeng Shen,
  • Songlin Zhao
YA-NAN HU
Zhejiang University of Technology Department of Applied Mathematics
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Shoufeng Shen
Zhejiang University of Technology Department of Applied Mathematics
Author Profile
Songlin Zhao
Zhejiang University of Technology Department of Applied Mathematics

Corresponding Author:[email protected]

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Abstract

Cauchy matrix approach for the discrete Ablowitz-Kaup-Newell-Segur equations is reconsidered, where two ‘proper’ discrete Ablowitz-Kaup-Newell-Segur equations and two ‘unproper’ discrete Ablowitz-Kaup-Newell-Segur equations are derived. The ‘proper’ equations admit local reduction, while the ‘unproper’ equations admit nonlocal reduction. By imposing the local and nonlocal complex reductions on the obtained discrete Ablowitz-Kaup-Newell-Segur equations, two local and nonlocal discrete complex modified Korteweg-de Vries equations are constructed. For the obtained local and nonlocal discrete complex modified Korteweg-de Vries equations, soliton solutions and Jordan-block solutions are presented by solving the determining equation set. The dynamical behaviors of 1-soliton solution are analyzed and illustrated. Continuum limits of the resulting local and nonlocal discrete complex modified Korteweg-de Vries equations are discussed.
Submitted to Mathematical Methods in the Applied Sciences
12 Jun 2024Submission Checks Completed
12 Jun 2024Assigned to Editor
20 Jun 2024Review(s) Completed, Editorial Evaluation Pending
09 Aug 2024Reviewer(s) Assigned
04 Nov 2024Editorial Decision: Accept