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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
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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.
12 Jun 2024Submission Checks Completed
12 Jun 2024Assigned to Editor
20 Jun 2024Review(s) Completed, Editorial Evaluation Pending
09 Aug 2024Reviewer(s) Assigned