We study stability of N-soliton solutions of the FPU lattice equation. Solitary wave solutions of FPU cannot be characterized as a critical point of conservation laws due to the lack of infinitesimal invariance in the spatial variable. In place of standard variational arguments for Hamiltonian systems, we use an exponential stability property of the linearized FPU equation in a weighted space w...

In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ; g2, g3)(g2, g3, invariants) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid ...

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...

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented. PACS number: 02. 03. Ik

It is shown that the generalized N=4 supersymmetric Toda lattice hierarchy contains the N=4 super-KdV hierarchy with the first flow time in the role of space coordinate. Two different N=2 superfield form of the generalized N=4 TL equation which are useful when solving the N=4 KdV and (1,1)-GNLS hierarchies are discussed.

The second part of the notes are written jointly with my collaborator from University of Illinois, M. B. Erdogan. We developed the material with two goals in mind. First to prove existence and uniqueness results in the case of dispersive PDE evolving from initial data that are periodic in the space variable. Secondly we develop new tools to address the problem of wellposedness of solutions, in ...

in the present article, a numerical method is proposed for the numerical solution of thekdv equation by using a new approach by combining cubic b-spline functions. in this paper we convert the kdv equation to system of two equations. the method is shown to be unconditionally stable using von-neumann technique. to test accuracy the error norms2l, ∞l are computed. three invariants of motion are p...

in this present work, the kudryashov method and the functional variable method are used to construct exact solutions of the complex kdv equation. the kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

We degenerate the finite gap solutions of the KdV equation from the general formulation in terms of abelian functions when the gaps tends to points, to recover solutions of KdV equations given a few years ago in terms of wronskians called solitons or positons. For this we establish a link between Fredholm determinants and Wronskians.

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equa...