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

2012/07/04 by Jonatan Lenells, Marcus Wunsch, Lenells, Jonatan +1
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Fractional Differential Equations Solutions #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1207.0968

Abstract

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

Citations

• Global existence and blow-up phenomena for the weakly dissipative Camassa–Holm equation
• The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations

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