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Conservation laws of the Camassa-Holm equation. (English) Zbl 1076.35100
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 mλ m . Moreover, a direct argument is presented proving that H -1 ,H -2 ,, 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 n s.
MSC:
35Q35PDEs in connection with fluid mechanics
37K05Hamiltonian structures, symmetries, variational principles, conservation laws