In this letter, a coupled system of viscous Burgers’ equations with zero Dirichlet boundary conditions and appropriate initial data is considered. For the well-known single viscous Burgers’ equation with zero Dirichlet boundary conditions, the zero equilibrium is the unique global exponential point attractor. A similar property is shown for the coupled Burgers’ equations, i.e., trajectories sta...

We have studied the phase dynamics in an oscillatory chemical system (Belousov-Zhabotinsky reaction). The phase distribution and isophase lines in the 2D phase space were reconstructed. The dynamics proved to be well described in terms of the Burgers equation. The phase dependence of the coefficients of the equation was taken into account to estimate the region of the applicability of the Burge...

An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which arise from the inexact linear system solvers. The theoretical investigations are illustrated numerically by an optimal control problem for the Burgers equation.

random burgers equation, random Hamilton-Jacobi equation, uniqueness of global minimizers We discuss a dynamical system approach to a problem of Burgers turbulence. It is shown that there exists a unique stationary distribution for solutions to spatially periodic inviscid random forced Burgers equation in arbitrary dimension. The construction is based on analysis of minimizing orbits for time-d...

The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg-de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report...

In this work, a composite numerical scheme based on finite difference and Haar wavelets is proposed to solve time dependent coupled Burgers’ equation with appropriate initial and boundary conditions. Time derivative is discretized by forward difference and then quasilinearization technique is used to linearize the coupled Burgers’ equation. Space derivatives discretization with Haar wavelets le...

In this report we observe several undesired behaviors of numerical schemes for the Burgers equation with a linear source term. Numerical solutions based on a splitting method are compared to exact solutions of the problem. method. From several examples we observe how some unexpected properties of numerical schemes grow and how they can be neutralized.

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differen...

Submitted: Mar 2, 2013; Accepted: Apr 10, 2013; Published: Jun 10, 2013 Abstract: In this article, we present a variant approach of the generalized and improved (G'/G)–expansion method and construct some new exact traveling wave solutions with free parameters of the nonlinear evolution equations, via the Painleve integrable Burgers equation, the Boiti-Leon-Pempinelle equation and the Pochhammer...