We investigate symmetries and reductions of a coupled KdV system with variable coefficients. The infinitesimals of the group of transformations which leaves the KdV system invariant and the admissible forms of the coefficients are obtained using the generalized symmetry method based on the Fréchet derivative of the differential operators. An optimal system of conjugacy inequivalent subgroups is...

We use asymptotic analysis and a near-identity normal form transformation from water wave theory to derive a 1+1 unidirectional nonlinear wave equation that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation. This equation is one order more accurate in asymptotic approximation beyond KdV, yet it still pr...

We prove that the Cauchy problem of the Schrödinger-KortewegdeVries (NLS-KdV) system for periodic functions is globally well-posed for initial data in the energy space H1×H1. More precisely, we show that the nonresonant NLS-KdV system is globally well-posed for initial data in Hs(T) × Hs(T) with s > 11/13 and the resonant NLS-KdV system is globally wellposed with s > 8/9. The strategy is to app...

The N = 2 supersymmetric α = 1 KdV hierarchy in N = 2 superspace is considered and its rich symmetry structure is uncovered. New nonpolynomial and nonlocal, bosonic and fermionic symmetries and Hamiltonians, bi-Hamiltonian structure as well as a recursion operator connecting all symmetries and Hamiltonian structures of the N = 2 α = 1 KdV hierarchy are constructed in explicit form. It is observ...

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equati...

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.