Local and nonlocal complex discrete and semi-discrete sine-Gordon equations and solutions

Abstract

In this paper, local and nonlocal complex reduction of a discrete and a semi-discrete negative order Ablowitz-Kaup-Newell- Segur equations is studied. Cauchy matrix type solutions, including soliton solutions and Jordan-block solutions, for the resulting local and nonlocal complex discrete and semi-discrete sine-Gordon equations are constructed. Dynamics of 1-soliton solution are analyzed and illustrated.

11 pages, 16 figures

References in corpus (2)

• Integrable $\mathcal{P}T$-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Solutions of local and nonlocal equations reduced from the AKNS hierarchy