The bifurcation analysis of the K (m, n) equation, which serves as a generalized model for the Korteweg-de Vries equation describing the dynamics of shallow water waves on ocean beaches and lake shores, is carried out in this paper. The phase portraits are given and solitary wave solutions are obtained. Singular periodic wave solutions are also given in this work.

We study the Bäcklund symmetry for the Moyal Korteweg-de Vries (KdV) hierarchy based on the Kuperschmidt-Wilson Theorem associated with second Gelfand-Dickey structure with respect to the Moyal bracket, which generalizes the result of Adler for the ordinary KdV. PACS: 02.30.Ik, 11.10.Ef

A new method for the computation of conserved densities of nonlinear differentialdifference equations is applied to Toda lattices and discretizations of the Korteweg-de Vries and nonlinear Schrödinger equations. The algorithm, which can be implemented in computer algebra languages such as Mathematica, can be used as an indicator of integrability.

Using one dimensional Quantum hydrodynamic (QHD) model Korteweg de Vries (KdV) solitary excitations of electron-acoustic waves (EAWs) have been examined in twoelectron-populated relativistically degenerate super dense plasma. It is found that relativistic degeneracy parameter influences the conditions of formation and properties of solitary structures. Keywords—Relativistic Degeneracy, Electron...

Nonlinear dispersive wave equations arise naturally in scientific and engineering fields such as fluid dynamics, electromagnetic theory, quantum mechanics, optical communication, nonlinear optics etc. Many important questions (both in theory and applications) are related to the interaction of two effects: energy spreading (dispersion, diffraction) and energy concentrating (nonlinear self-trappi...

We numerically study nonlinear dispersive wave equations of generalized Kadomtsev-Petviashvili type in the regime of small dispersion. To this end we include general power-law nonlinearities with different signs. A particular focus is on the Korteweg-de Vries sector of the corresponding solutions. version: October 26, 2006

The conserved polynomials of the Korteweg–de Vries equation ut = uxxx − 12uux are characterized by the vanishing of the residues of their associated differential polynomials evaluated on the formal power series of the kind u = x−2 + u0 + ∑ n≥2 unx.