Author
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date
2016
Publication Place
-
Informa Group
Subject
Generalized Camassa-Holm equation, Modified Camassa-Holm equation, Fractional Camassa-Holmequation, Improved Boussinesq equation, Asymptotic expansions
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1776-0852
Record ID
3e1c4ab9-94df-47e7-b732-f4c8500db360
Library Location
Natural and Mathematical Sciences
Date
2016
Sample Text
In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type equation using a two-parameter 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 power-type nonlinearity while the second one replaces the dispersive terms of the CH equation with fractional-type dispersive terms. In the absence of both higher-order nonlinearities and fractional-type 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.
DOI
10.1080/14029251.2016.1199493
Cilt
23
