It is pointed out that for the case of (compressible) magnetohydrodynamics (MHD) with the fields v y (y, t) and B x (y, t) one can have equations of the Burgers type which are integrable. We discuss the solutions. It turns out that the propagation of the non-linear effects is governed by the initial velocity (as in the Burgers case) as well as by the initial Alfvén velocity. Many results previo...

Exact solutions and dynamics of globally coupled phase oscillators 2 Abstract. We analyze mean-field models of synchronization of phase oscillators with singular couplings and subject to external random forces. They are related to the Kuramoto-Sakaguchi model. Their probability densities satisfy local partial differential equations similar to the Porous Medium, Burgers and extended Burgers equa...

We present a noncommutative version of the Burgers equation which possesses the Lax representation and discuss the integrability in detail. We find a noncommutative version of the Cole-Hopf transformation and succeed in the linearization of it. The linearized equation is the (noncommutative) diffusion equation and exactly solved. We also discuss the properties of some exact solutions. The resul...

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...

in this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation.this method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation and c...

The vortex stretching process is relevant to energy transport at various scales in turbulent flow and in vortex reconnection. For these, reasons, exact solutions for vortex flow are useful. Robinson and Saffman [1] examined the Burgers vortex solution and found closed form steady solutions for special parameter values. Unsteady 2D Burgers vortex solutions have been used to model the spanwise st...

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...

Burgers’ equation frequently appears in the study of turbulence theory, as well as some other scientific fields. High and low Reynolds numbers play important roles in both modeling and numerical simulation. In this paper, we apply a numerical scheme to solve a two-dimensional time-fractional Burgers equation. The key feature of the proposed method is formed by combining the discontinuous Galerk...

The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley eq...

In this work, the G G        -expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the G G        -expansion method provides not only more general forms of solutions but als...