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Zbl 1076.35100
Lenells, Jonatan
Conservation laws of the Camassa-Holm equation. (English)
[J] J. Phys. A, Math. Gen. 38, No. 4, 869-880 (2005). ISSN 0305-4470

Summary: We use the bi-Hamiltonian structure of the Camassa--Holm equation to show that its conservation laws $H_n[m]$ are homogeneous with respect to the scaling $m \mapsto \lambda_m$. Moreover, a direct argument is presented proving that $H_{-1}, H_{-2}, \dots$, are of local character. Finally, simple representations of the conservation laws in terms of their variational derivatives are derived and used to obtain a constructive scheme for computation of the $H_ns$.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
37K05 Hamiltonian structures, etc.

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Zentralblatt MATH Berlin [Germany]