2011/02/28 by N. H. Ibragimov, Nail H. Ibragimov, Ibragimov, N. H. +5
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1102.5719
openalex publication_date 2011/02/28 · arxiv created 2011/04/01 · arxiv updated 2011/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that the Camassa-Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, Ibragimov has shown that the KdV and the modified KdV equations are self-adjoint. Starting from the generalization of the Camassa-Holm equation, we prove that the Camassa-Holm equation is self-adjoint. This property is important, e.g. for constructing conservation laws associated with symmetries of the equation in question. Accordingly, we construct conservation laws for the generalized Camassa-Holm equation using its symmetries.