This paper deals with the Burgers equation which is most common model used in nonlinear conservation laws. Here theoretical aspect of law discussed by using inviscid equation. At first, we introduce general non-linear as a partial differential and its solution procedure method characteristic. Next, present weak problem entropy condition. Taking into account shock wave rarefaction wave, Riemann ...

By the Cole-Hopf transformation, with any linear evolution equation in 1 + 1 dimensions a generalized Burgers equation is associated. We describe local conservation laws of these equations. It turns out that any generalized Burgers equation has only one conservation law, while a linear evolution equation with constant coefficients has an infinite number of (x, t)independent conservation laws if...

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...

Head on collision of localized waves in cold and dense hadronic matter with and without shear and bulk viscosities is investigated. Non-relativistic dynamics of propagating waves is studied using the hydrodynamics description of the system and suitable equation of state. It will be shown that the localized waves are described by solutions of the Burgers equation. Simulations show that the propa...

Higher-order accurate finite-difference schemes for solving the unsteady Burgers’ equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented. The unsteady Burgers’ equation belongs to a few nonlinear partial differential equations which has an exact solution, and it allows one to compare the numerical solution with the exact one, and the properti...

A generalization of the Hopf–Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimen...

The dust-acoustic shock waves have been theoretically investigated using reductive perturbation technique. An unmagnetized four-component dusty plasma system consisting of nonextensive q-distributed electrons, Boltzmann distributed ions, and negatively as well as positively charged dust particles has been considered. The solution of Burgers equation in planar geometry is numerically analyzed. I...

In this paper we construct a stochastic particle method for the Burgers equation with a monotone initial condition; we prove that the convergence rate is O(1= p N + p t) for the L 1 (IR)-norm of the error. To obtain that result, we link the PDE and the algorithm to a system of weakly interacting stochastic particles; the diiculty of the analysis comes from the discontinuity of the interaction k...

In this paper we study the dynamics of a Burgers’ type equation (1.1). First, we use a new method called attractor bifurcation introduced by Ma and Wang in [4, 6] to study the bifurcation of Burgers’ type equation out of the trivial solution. For Dirichlet boundary condition, we get pitchfork attractor bifurcation as the parameter λ crosses the first eigenvalue. For periodic boundary condition,...