Integrability Test and Travelling-Wave Solutions of Higher-Order Shallow- Water Type Equations

Recently, a considerable number of analytic methods have been successfully developed and applied for constructing exact travelling wave so- lutions to nonlinear evolution equations

(24) For this last equation we thus obtain two travelling- wave solutions, given by substituting µ = α in (21), where α is one of the two positive real roots of (23) (we can choose

In this work we study two partial differential equations that constitute second- and third-order approximations of water wave equations of the Korteweg – de Vries type. In

In this paper we have used a simple assump- tion and have found new solitary wave solutions for equations (1.4) and (1.5), that represent, respectively, second- and

We have suggested the mixed dn-sn method and used it to construct multiple periodic wave solutions for a variety of nonlinear wave equations.. We ap- plied this method to the

The local existence and uniqueness of solutions was shown in [2] for a one-dimensional setting with insulating boundary conditions, and for the case of higher dimensions with

Seen from another point of view, these Fourier coefficients can be construed as radially symmetric solutions to n–dimensional wave equations with different inverse–square potentials,

It is a particular case of a thermoelastic system given by a coupling of a plate equation to a hyperbolic heat equation arising from Cattaneo’s law of heat conduction.. In a