2024/02/20 by Ziqi Li, Kai Tian, Li, Ziqi +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2402.12618
openalex publication_date 2024/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a 2-component Camassa-Holm equation, as well as a 2-component generalization of the modified Camassa-Holm equation, nonlocal infinitesimal symmetries quadratically depending on eigenfunctions of linear spectral problems are constructed from functional gradients of spectral parameters. With appropriate pseudo-potentials, these nonlocal infinitesimal symmetries are prolonged to enlarged systems, and then explicitly integrated to generate symmetry transformations in finite form for enlarged systems. As implementations of these finite symmetry transformations, some kinds of nontrivial solutions and Bäcklund transformations are derived for both equations.