An action is constructed that gives an arbitrary equation in the KdV or MKdV hierarchies as equation of motion; the second Hamiltonian structure of the KdV equation and the Hamiltonian structure of the MKdV equation appear as Poisson bracket structures derived from this action. Quantization of this theory can be carried out in two different schemes, to obtain either the quantum KdV theory of Ku...

In this paper, an analytical approximation to the solution of higher order Korteweg-de Vries (KdV) equations has been studied. The Homotopy Perturbation Method (HPM) introduced by He is employed to drive this analytical solution and the results will be compared with those of the Adomian decomposition method. Numerical results reveal that the HPM provides highly accurate numerical solutions for ...

In this paper, the variational iteraton method is used for solving the Generalized HirotaSatsuma Coupled KdV ( GHS KdV ) equations. In this method general Lagrange multipliers are introduced to construct correction functionals for the models.In the current paper, we are applied this technique on interesting and important model.The results are compared with exact solution.

We consider the stochastic quantization scheme for a non-perturbative stabilization of 2D quantum gravity and prove that it does not satisfy the KdV flow equations. It therefore differs from a recently suggested matrix model which allows real solutions to the KdV equations. The behaviour of the Fermi energy, the free energy and macroscopic loops in the stochastic quantization scheme are elucida...

We propose a hamiltonian formulation of the N = 2 supersym-metric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian structure which allows for several reductions of the KP type hierarchy. In particular, the third family of N = 2 KdV hierarchies is recovered. We also give an easy constrution of Wronskian solutions of the KP and KdV type equations.

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani, Hirota-Satsuma). The solutions for multiple collisions of super-solitons and extension to SUSY sine-Gordon are also discussed.

This paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg-de Vries (KdV) equation from boundary measurements of a single solution. The Lipschitz stability of this inverse problem is obtained using a new global Carleman estimate for the linearized KdV equation. The proof is based on the Bukhgĕım-Klibanov method.

In this Letter, based on the idea of homogeneous balance (HB) method and with help of MATHEMATICA, we obtain a new auto-Bäcklund transformation for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order. Then based on the Bäcklund transformation, some solutions for these two equations are derived.  2002 Elsevier Science B.V. All rights reserved.

The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota–Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.

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