Adiabatic invariants of the extended KdV equation

New analytical soliton type solutions for double layers structure model of extended KdV equation

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...

The Extended Generalized Riccati Equation Mapping Method for the (1+1)-Dimensional Modified KdV Equation

where p,q and r are arbitrary constants. We construct twenty five exact traveling wave solutions of the (1+1)-dimensional modified KdV equation involving parameter by applying this method. The solutions are presented in terms of the hyperbolic, the trigonometric and the rational functional form including solitons and periodic solutions. Moreover, it is worth mentioning that one of our obtained ...

Theory of Adiabatic Invariants

We review the basic theory on adiabatic invariants in classical and quantum mechanics. PACS numbers: 45.30.+s,05.45.-a,03.65.-w, 03.65.Sq

Notes on Adiabatic Invariants

Multi-soliton of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and KdV equation

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...