2024/04/22 by Ya-Nan Hu, Hu, Ya-Nan, Shoufeng Shen +3 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Electromagnetic Simulation and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2404.14150
openalex publication_date 2024/04/22 · openalex created_date 2024/04/24 · openalex updated_date 2026/07/28
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.