The goal of this paper is to calculate of order reduction of the KdV typeequation and the non-isospectral KdV type equation using the μ-symmetrymethod. Moreover we obtain μ-conservation law of the non-isospectral KdVtype equation using the variational problem method.

An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura's transformation connecting the KdV and mKdV equations is studied in detail. 1. Introduction Our aim in this note is to display the close similarity between the well-known Cole{Hopf transformation relating the Burgers and the heat equation, and the celebrated Miura trans...

In this paper we construct a family of commuting multidimen-sional differential operators of order 3, which is closely related to the KdV hierarchy. We find a common eigenfunction of this family and an algebraic relation between these operators. Using these operators we associate a hy-perelliptic curve to any solution of the stationary KdV equation. A basic generating function of the solutions ...

A two-way linear mixed model with three variance components as 1, 2 2 and 2 e is applied to evaluate the performance of modi…ed Henderson’s method 3 developed by Al-Sarraj and Rosen (2007). The focus of modi…ed procedure is on the estimation of 1 which variance components is mainly concerned. The modi…ed estimator is expected to perform better than unmodi…ed Henderson’s method 3 in terms of MSE...

where μ, ν are positive constants. This equation, in the case μ = 0, was derived independently by Sivashinsky [1] and Kuramoto [2] with the purpose to model amplitude and phase expansion of pattern formations in different physical situations, for example, in the theory of a flame propagation in turbulent flows of gaseous combustible mixtures, see Sivashinsky [1], and in the theory of turbulence...

We study the small dispersion limit for the Korteweg-de Vries (KdV) equation ut + 6uux + ǫ uxxx = 0 in a critical scaling regime where x approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to ...

In this paper the stability of the Korteweg-de Vries (KdV) equation is investigated. It is shown analytically and numerically that small perturbations of solutions of the KdV-equation introduce effects of dispersion, hence the perturbation propagates with a different velocity then the unperturbed solution. This effect is investigated analytically by formulating a differential equation for pertu...

For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations. The reduction of one of the Bäcklund–Darboux transformations and the corresponding discrete system are considered for Kupershmidt’s super KdV equation....

is paper reports the strain sensitivity of �exible, electrically conductive, and nanostructured cellulose which was prepared by modi�cation of bacterial cellulose with double-walled carbon nanotubes (DWCNTs) and multiwalled carbon nanotubes (MWCNTs).e electrical conductivity depends on themodifying agent and its dispersion process.e conductivity of the samples obtained from bacterial cellulo...