The main objective of this article is to analyse the dynamics of Burgers equation on the unit interval, driven by affine linear white noise. It is shown that the solution field of the stochastic Burgers equation generates a smooth perfect and locally compacting cocycle on the energy space L2([0, 1],R). Using multiplicative ergodic theory techniques, we establish the existence of a discrete non-...

We define the Burgers superprocess to be the solution of the stochastic partial differential equation ∂ ∂t u(t, x) =∆u(t, x) − λu(t, x)∇u(t, x) + γ √ u(t, x) W (dt, dx), where t ≥ 0, x ∈ R, and W is space-time white noise. Taking γ = 0 gives the classic Burgers equation, an important, non-linear, partial differential equation. Taking λ = 0 gives the super Brownian motion, an important, measure ...

A non-isotropic version of phase equations such as the Burgers equation, the K-dV-Burgers equation, the Kuramoto-Sivashinsky equation and the Benney equation in the three-dimensional space is systematically derived from a general reaction-diffusion system by means of the renormalization group method. PACS codes: 47.20.Ky

This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV–Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method. 2010 Elsevier Inc. All rights reserved.

The Burgers equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank Nicholson, used for solving the one-dimensional Burgers equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to the conve...

New solutions of some important partial differential equations are obtained using the first integral method. The efficiency of the method is demonstrated by applying it for the linear Klein-Gordan equation, MKdV equation, Burgers’ equation in two and three dimensions.

Approximation theorems, analogous to known results for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for a nonlinear parabolic equation, Burgers’ equation.

We continue to study a simple integro-differential equation: the Quasi-Steady equation (QS) of flame front dynamics. This second order quasi-linear parabolic equation with a non-local term is dynamically similar to the Kuramoto-Sivashinsky (KS) equation. In [FGS03], where it was introduced, its well-posedness and proximity for finite time intervals to the KS equation in Sobolev spaces of period...