1. Solutions of local and nonlocal discrete complex modified Korteweg-de Vries equations and continuum limits
- Author
-
Hu, Ya-Nan, Shen, Shou-Feng, and Zhao, Song-lin
- Subjects
Nonlinear Sciences - Exactly Solvable and Integrable Systems - 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., Comment: This paper contains 18 pages and 14 figures
- Published
- 2024