Derivation of generalized CamassaHolm equations from Boussinesqtype equations
Erbay, Hüsnü Ata and Erbay, Saadet and Erkip, Albert (2016) Derivation of generalized CamassaHolm equations from Boussinesqtype equations. (Accepted/In Press) AbstractIn this paper we derive generalized forms of the CamassaHolm (CH) equation from a Boussinesqtype equation using a twoparameter asymptotic expansion based on two small parameters characterizing nonlinear and dispersive
effects and strictly following the arguments in the asymptotic derivation of the classical CH equation. The resulting equations generalize the CH equation in two different ways. The first generalization replaces the quadratic nonlinearity of the CH equation with a general powertype nonlinearity while the second one replaces the dispersive terms of the CH equation with fractionaltype dispersive terms. In the absence of both higherorder nonlinearities and fractionaltype dispersive effects, the generalized equations derived reduce to the classical CH equation that describes unidirectional propagation of shallow water waves. The generalized
equations obtained are compared to similar equations available in the literature, and this leads to the observation that the present equations have not appeared in the literature. Item Type:  Article 

Uncontrolled Keywords:  Generalized CamassaHolm equation; modified CamassaHolm equation; fractional CamassaHolm equation; improved Boussinesq equation; asymptotic expansions 

Subjects:  Q Science > QA Mathematics > QA299.6433 Analysis 

ID Code:  29280 

Deposited By:  Albert Erkip 

Deposited On:  13 Apr 2016 11:26 

Last Modified:  03 Nov 2016 11:35 

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