Electron. J. Diff. Eqns., Vol. 2003(2003), No. 05, pp. 1-12.

Stability of peakons for the generalized Camassa-Holm equation

Orlando Lopes

We study the existence of minimizers for a constrained variational problems in $H^1(\mathbb{R})$. These minimizers are stable waves solutions for the Generalized Camassa-Holm equation, and their derivative may have a singularity (in which case the travelling wave is called a peakon). The existence result is based on a method developed by the same author in a previous work. By giving examples, we show how our method works.

Submitted October 25, 2002. Published January 7, 2003.
Math Subject Classifications: 35J20, 49J10.
Key Words: variational problems, stability of peakons.

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Orlando Lopes
Departamento de Matematica-IMECC-UNICAMP-
C.P. 6065 Campinas, SP 13083-859, Brasil
e-mail: lopes@ime.unicamp.br
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