In this letter, a Painlevé integrable coupled KdV equation is proved to be also Lax integrable by a prolongation technique. The Miura transformation and the corresponding coupled modified KdV equation associated with this equation are derived. © 2010 Published by Elsevier Ltd

We present the results of further analysis of the integrability properties of the N = 4 supersymmetric KdV equation deduced earlier by two of us (F.D. & E.I., Phys. Lett. B 309 (1993) 312) as a hamiltonian flow on N = 4 SU(2) superconformal algebra in the harmonic N = 4 superspace. To make this equation and the relevant hamiltonian structures more tractable, we reformulate it in the ordinary N ...

in this paper , the quintic b-spline collocation scheme is employed to approximate numerical solution of the kdv-like rosenau equation . this scheme is based on the crank-nicolson formulation for time integration and quintic b-spline functions for space integration . the unconditional stability of the present method is proved using von- neumann approach . since we do not know the exact solution...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...

We provide a rigorous treatment of continuous limits for various generalizations the pentagram map on polygons in RPd by means quantum calculus. Describing this limit detail case short-diagonal map, we verify that construction yields (2,d+1)-KdV equation, and moreover, Lax form is proved to become representation corresponding KdV system. More generally, introduce χ-pentagram geometric defining ...

This paper aims to investigate an approximate-analytical and numerical solutions for some 1D 2D dispersive homogeneous non-homogeneous KdV equations by employing two reliable methods namely reduced differential transform method (RDTM) a classical finite-difference method. RDTM provides analytical approximate solution in the form of convergent series. The (FDM) solve is employed primarily checki...

In this paper, tanh method is applied to obtain exact solutions for two systems of nonlinear wave equations, namely, two component evolutionary system of homogeneous KdV equations of order 3 (type I as well as type II). Moreover, traveling wave hypothesis is used to obtain sech solution of type II coupled KdV system, in a more general setting. The results show that this method presents exact so...

Abstract: In this paper, the homotopy perturbation method (HPM) is applied to obtain approximate solutions to three systems of nonlinear wave equations, namely, two component evolutionary system of a homogeneous KdV equations of order 3 (type I) as well as (type II), and the generalized coupled Hirota Satsuma KdV. The numerical results show that this method is a powerful tool for solving system...

The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system – open-closed string theory. Nonperturbative solutions of the multi-critical unitary matrix models map to nonsingular solutions of the ‘renormalisation group’ equation for the string susceptibility, [P̃ , Q] =Q . We also demonstrate that the large N solutions of unitary matr...