The extended forced Korteweg-de Vries equation (efKdV) is a mathematical model for simulating the interaction of a shallow layer of fluid with external forcing agents. Herein we consider the dynamics of the efKdV when the forcing is assumed to be small and spatially periodic with a timeperiodic variation of the phase. We show that a good heuristic understanding of the dynamics for a certain cla...

The theory of evolution equations in Hamiltonian form is developed by use of some differential complexes arising naturally in the formal theory of partial differential equations. The theory of integral invariants is extended to these infinitedimensional systems, providing a natural generalization of the notion of a conservation law. A generalization of Noether's theorem is proved, giving a one-...

In this paper, we derive a Bäcklund transformation for the supersymmetric Korteweg-de Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Korteweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 19...

We solve the Vlasov equation for the longitudinal distribution function and find stationary wave patterns when the distribution in the energy error is Maxwellian. In the long wavelength limit a stability criterion for linear waves has been obtained and a Korteweg-de VriesBurgers equation for the relevant hydrodynamic quantities has been derived. Paper presented at Workshop on Instabilities of H...

We solve the Vlasov equation for the longitudinal distribution function and nd stationary wave patterns when the distribution in the energy error is Maxwellian. In the long wavelength limit a stability criterion for linear waves has been obtained and a Korteweg-de VriesBurgers equation for the relevant hydrodynamic quantities has been derived. Paper presented at Workshop on Instabilities of Hig...

On the exact solutions of integrable models, there is a new classification way recently based on the property of associated spectral parameters [1]. Negatons, related to the negative spectral parameter, are usually expressed by hyperbolic functions, and positons are expressed by means of trigonometric functions related to the positive spectral parameters. The so-called complexiton, which is exp...

This paper intends to look at the influence of rapidly varying regions on propagation internal undular bores in a two-layer fluid flow. Internal have been observed ocean around world. The appropriate mathematical model describe evolution stratified is variable-coefficient extended Korteweg-de Vries equation. governing equation solved numerically using method lines simulate bores. Our numerical ...