This class of equations was introduced by Kichenassamy and Olver [16]. It contains in particular the Kawahara equation [14] introduced to model magneto-acoustic waves, the various models derived by Olver [18] for the unidirectional propagation of waves in shallow water when the third order term appearing in the Korteweg-de Vries equation is small, and many other models. See [16] for a discussio...

The Korteweg-de Vries equation models the formation of solitary waves in context shallow water a channel. In Equation (1), f or p=2 and p=3 (Korteweg-de equations (KdV)) (modified (mKdV) respectively), these have many applications Physics. (gKdV) is Hamiltonian system. this article we investigate generalized (3). A new topological approach applied to prove existence at least one classical solut...

The transformation of a weakly nonlinear interfacial solitary wave in an ideal twolayer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a we...

In this present study the double layers structure model of extended Korteweg-de Vries(K-dV) equation will be obtained with the help of the reductive perturbation method, which admits a double layer structure in current plasma model. Then by using of new analytical method we obtain the new exact solitary wave solutions of this equation. Double layer is a structure in plasma and consists of two p...