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...

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.

In Section 1 we present a general principle for associating nonlinear equations of evolutions with linear operators so that the eigenvalues of the linear operator are integrals of the nonlinear equation. A striking instance of such a procedure is the discovery by Gardner, Miura and Kruskal that the eigenvalues of the Schrodinger operator are integrals of the Korteweg-de Vries equation. In Secti...

In most of the studies concerning nonlinear wave equations Korteweg-de Vries type, authors focus on waves elevation. Such have general form ~$u_{\text{u}}(x,t)=A f(x-vt)$, where ~$A>0$. this communication we show that if ~$u_{\text{up}}(x,t)=A f(x-vt)$ is solution a given equation, then $u_{\text{down}}(x,t)=-A is, an inverted same but with changed sign parameter ~$\alpha$. This property common...

Stationary wave solutions of the perturbed Korteweg-de Vries equation are considered in the presence of external hamiltonian perturbations. Conditions of their chaotic behaviour are studied with the help of Melnikov theory. For the homoclinic chaos Poincaré sections are constructed to demonstrate the complicated behaviour, and Lyapunov exponents are also numerically calculated.

Convergence and quasi-optimality of an adaptive finite element method for controlling L2 errors ⋆ Alan Demlow1, Rob Stevenson2 1 Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506–0027 ([email protected]) 2 Korteweg-de Vries (KdV) Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands (R.P.Stevenson@...

In recent years two nonlinear dispersive partial differential equations have attracted much attention due to their integrable structure. We prove that both equations arise in the modeling of the propagation of shallow water waves over a flat bed. The equations capture stronger nonlinear effects than the classical nonlinear dispersive Benjamin–Bona–Mahoney and Korteweg–de Vries equations. In par...

In this paper we consider the initial boundary value problem of the Korteweg-de Vries equation posed on a finite interval ut + ux + uxxx + uux = 0, u(x, 0) = φ(x), 0 < x < L, t > 0 (0.1) subject to the nonhomogeneous boundary conditions, B1u = h1(t), B2u = h2(t), B3u = h3(t) t > 0 (0.2)

In this paper, an efficient numerical schemes based on the Haar wavelet method are applied for finding numerical solution of nonlinear third-order modified Korteweg-de Vries (mKdV) equation as well as modified Burgers’ equations. The numerical results are then compared with the exact solutions. The accuracy of the obtained solutions is quite high even if the number of calculation points is small.