Remarks on the conserved densities of the Camassa-Holm equation

Details Remarks on the conserved densities of the Camassa-Holm equation Remarks on the conserved densities of the Camassa-Holm equation

2006-09-25

arxiv.org/abs/nlin/0609060v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

5 pages, submitted to J. Phys.A: Math.Gen

Scientific paper

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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