In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the case of the gaussian unitary ensemble, on which we focus in this paper, we show that the characteristics polynomials and their inverse evolve according to a...

In this paper, we use a kind of univariate multiquadric (MQ) quasi-interpolation to solve partial differential equation (PDE). We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the r...

A bottleneck situation in one-lane traffic flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal realization of this mechanism to which we refer to as density-feedback control (DFC): If the actual density in the bottleneck is above a certain threshold, t...

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.

Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended G G ′       -expansion method, substituting the solutions obtained into the cor...

The Burgers’ equation first appeared in the paper by Bateman [3], who mentioned two of the essentially steady solutions. Due to extensive works of Burgers [4] involving the Burgers’ equation especially as a mathematical model for the turbulence, it is known as Burgers’ equation. The equation is used as a model in fields as wide as heat conduction [5], gas dynamics [13], shock waves [4], longitu...

In this paper, a two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform d...

Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...