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

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.

preprint2012arXivOpen access
Jonatan LenellsMarcus Wunsch
math.AP
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Open access2 authors1 topic
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Jonatan LenellsMarcus Wunsch

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