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math-ph2022★ 1 cited
On the full dispersion Kadomtsev-Petviashvili equations for dispersive elastic waves
H. A. Erbay, S. Erbay, A. Erkip
Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev-Petviashvili (KP) equation, are interesting from both the physical and mathema…
math-ph2016
Derivation of Generalized Camassa-Holm Equations from Boussinesq-type Equations
H. A. Erbay, S. Erbay, A. Erkip
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…
math-ph2015★ 21 cited
Derivation of the Camassa-Holm equations for elastic waves
H. A. Erbay, S. Erbay, A. Erkip
In this paper we provide a formal derivation of both the Camassa-Holm equation and the fractional Camassa-Holm equation for the propagation of small-but-finite amplitude long waves…