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arXiv · 1207.0968

On the weakly dissipative Camassa-Holm, Degasperis-Procesi, and Novikov equations

Jonatan Lenells·Marcus Wunsch
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Abstract

We show that the weakly dissipative Camassa-Holm, Degasperis-Procesi, Hunter-Saxton, and Novikov equations can be reduced to their non-dissipative versions by means of an exponentially time-dependent scaling. Hence, up to a simple change of variables, the non-dissipative and dissipative versions of these equations are equivalent. Similar results hold also for the equations in the so-called b-family of equations as well as for the two-component and μ-versions of the above equations.

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Jonatan Lenells, Marcus Wunsch. 2012-07-04. On the weakly dissipative Camassa-Holm, Degasperis-Procesi, and Novikov equations. https://arxiv.org/abs/1207.0968

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