In this paper, we present homotopy perturbation method (HPM) for solving the Korteweg-de Vries (KdV) equation and convergence study of homotopy perturbation method for nonlinear partial differential equation. We compared our solution with the exact solution and homotopy analysis method (HAM). The results show that the HPM is an appropriate method for solving nonlinear equation.

Some techniques of bilinearization of the non-autonomous 1 + 1 dimensional discrete soliton equations is discussed by taking the discrete KdV equation, the discrete Toda lattice equation, and the discrete LotkaVolterra equation as examples. Casorati determinant solutions to those equations are also constructed explicitly.

We construct various periodic travelling wave solutions of the Ostrovsky/HunterSaxton/short pulse equation and its KdV regularized version. For the regularized short pulse model with small Coriolis parameter, we describe a family of periodic travelling waves which are a perturbation of appropriate KdV solitary waves. We show that these waves are spectrally stable. For the short pulse model, we ...

This paper investigates the implementation of Variational Iteration Method (VIM) to practical and higher order nonlinear equations in kind of Korteweg-de-Vries (KdV) equation. The obtained solutions from thirdand fourth-order modified KdV are compared with the exact and Homotopy Perturbation Method (HPM) solutions. Results illustrate the efficiency and capability of VIM to solve high order nonl...

We construct various periodic travelling wave solutions of the Ostrovsky/HunterSaxton/short pulse equation and its KdV regularized version. For the regularized short pulse model with small Coriolis parameter, we describe a family of periodic travelling waves which are a perturbation of appropriate KdV solitary waves. We show that these waves are spectrally stable. For the short pulse model, we ...

The solutions of the Cauchy problem KdV equation on a periodic domain

We show that Novikov–Veselov equation (an analog of KdV in dimension 2 + 1) does not have exponentially localized solitons at negative energy.

We present a simple a direct proof of the complete integrability of the quantum KdV equation at c = −2, with an explicit description of all the conservation laws.

Unspecified Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: http://doi.org/10.5167/uzh-22229 Originally published at: Bättig, D; Kappeler, T; Mityagin, B (1997). On the Korteweg-de Vries equation: frequencies and initial value problem. Pacific Journal of Mathematics, 181(1):1-55. pacific journal of mathematics Vol. 181, No. 1, 1997 ON THE KORTEWEG-DE VRIES EQUAT...

McKean and Trubowitz [2] showed that the theory of the KdV equation ∂ ∂t g(x, t) = ∂ 3 ∂x 3 g(x, t) − 6g(x, t) ∂g ∂x (x, t). is intimately related to the geometry of a related hyperelliptic curve of infinite genus, the Bloch spectrum B g t of the operator L g t : ψ → d 2 dx 2 ψ(x) + g(x, t)ψ(x), where g t = g(x, t). As was known classically, B g t is independent of t, when g(x, t) evolves accor...