Work

Solutions of Local and Nonlocal Discrete Complex Modified Korteweg–De Vries Equations and Continuum Limits

Year: 2024

Type: article

Abstract: 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.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10619

Authors: Ya‐nan Hu, Shou‐feng Shen, Song‐lin Zhao

Institution: Zhejiang University of Technology

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $4,760

Funders: National Natural Science Foundation of China, Natural Science Foundation of Zhejiang Province