2023/07/19 by Han‐Han Sheng, Bao‐Feng Feng, Sheng, Han-Han +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2307.10497
openalex publication_date 2023/07/19 · openalex created_date 2023/07/22 · openalex updated_date 2026/07/28
In this paper, we propose fully discrete analogues of a generalized sine-Gordon (gsG) equation ut x=(1+ν∂x2) sin u. The bilinear equations of the discrete KP hierarchy and the proper definition of discrete hodograph transformations are the keys to the construction. Then we derive semi-discrete analogues of the gsG equation from the fully discrete gsG equation by taking the temporal parameter b→0. Especially, one full-discrete gsG equation is reduced to a semi-discrete gsG equation in the case of ν=-1 (Feng \it et al. Numer. Algorithms 2023). Furthermore, N-soliton solutions to the semi- and fully discrete analogues of the gsG equation in the determinant form are constructed. Dynamics of one- and two-soliton solutions for the discrete gsG equations are discussed with plots. We also investigate the reductions to the sine-Gordon (sG) equation and the short pulse (SP) equation. By introducing an important parameter c, we demonstrate that the gsG equation reduces to the sG equation and the SP equation, and the discrete gsG equation reduces to the discrete sG equation and the discrete SP equation, respectively, in the appropriate scaling limit. The limiting forms of the N-soliton solutions to the gsG equation also correspond to those of the sG equation and the SP equation.