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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Lenells, Jonatan¹  Wunsch, Marcus² 

[1] Baylor Univ, Dept Math, Waco, TX 76798 USA

[2] Swiss Fed Inst Technol, Dept Math, CH-8092 Zurich, Switzerland

关键词: Weak dissipation;    Camassa-Holm equation;    Degasperis-Procesi equation;    Novikov equation;   

DOI  :  10.1016/j.jde.2013.04.015

来源: Elsevier

【 摘 要 】

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 mu-versions of the above equations. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free