Conservation laws for Camassa-Holm equation, Dullin-Gottwald-Holm equation and generalized Dullin-Gottwald-Holm equation. (English) Zbl 1179.35275

Summary: We construct the conservation laws for the Camassa-Holm equation, the Dullin-Gottwald-Holm equation (DGH) and the generalized Dullin-Gottwald-Holm equation (generalized DGH). The variational derivative approach is used to derive the conservation laws. Only first order multipliers are considered. Two multipliers are obtained for the Camassa-Holm equation. For the DGH and generalized DGH equations the variational derivative approach yields two multipliers; thus two conserved vectors are obtained.


35Q51 Soliton equations
35C05 Solutions to PDEs in closed form
35A15 Variational methods applied to PDEs
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