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Remarks on the conserved densities of the Camassa-Holm equation

Amitava Choudhuri·B. Talukdar·S. Ghosh
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Abstract

It is pointed out that the higher-order symmetries of the Camassa-Holm (CH) equation are nonlocal and nonlocality poses problems to obtain higher-order conserved densities for this integrable equation (J. Phys. A: Math. Gen. 2005, {\bf 38} 869-880). This difficulty is circumvented by defining a nolinear hierarchy for the CH equation and an explicit expression is constructed for the nth-order conserved density.

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Amitava Choudhuri, B. Talukdar, S. Ghosh. 2006-09-25. Remarks on the conserved densities of the Camassa-Holm equation. https://arxiv.org/abs/nlin/0609060

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