2021/10/29 by Han‐Han Sheng, Han-Han Sheng, Guo‐Fu Yu +6
Mathematics · Physics and Astronomy · #35C08 #35Q51 #39A36 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP #msc:35C08 #msc:35Q51 #msc:39A36 #nlin.SI
paper · pdf · doi:10.48550/arxiv.2110.15876
26 pages, 2 figures
arxiv created 2021/10/29 · openalex publication_date 2021/10/29 · arxiv updated 2021/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In the present paper, we are concerned with integrable discretization of a modified Camassa-Holm equation with linear dispersion term. The key of the construction is the semi-discrete analogue for a set of bilinear equations of the modified Camassa-Holm equation. Firstly, we show that these bilinear equations and their determinant solutions either in Gram-type or Casorati-type can be reduced from the discrete KP equation through Miwa transformation. Then, by scrutinizing the reduction process, we obtain a set of semi-discrete bilinear equations and their general soliton solution in Gram-type or Casorati-type determinant form. Finally, by defining dependent variables and discrete hodograph transformations, we are able to derive an integrable semi-discrete analogue of the modified Camassa-Holm equation. It is also shown that the semi-discrete modified Camassa-Holm equation converges to the continuous one in the continuum limit.