In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.

In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solut...

This paper examines the properties of a regularization of the Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as the convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multip...

We propose a new approach for the analysis of stationary correlation functions of 1D Burgers equation driven by a random force. We use this to study the asymptotic behavior of the probability distribution of velocity gradients and velocity increments. PACS number 47.27.Gs, 03.40.Gc Statistical properties of solutions of random forced Burgers equation have been a subject of intensive studies rec...

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.

They are of first order, second order, third order 27 and fourth order, respectively. The third-order Burg28 ers equation, similar to the second-order ones, appear 29 in many physical and engineering fields [8–10], such 30 as the plasma physics and fluid mechanics. In addi31 tion, these equations play a key role in nonlinear the32 ory and mathematical physics, in particular in the inte33 grable...

In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.

Intermittency effects in Burgers equation driven by thermal noise. Abstract For the Burgers equation driven by thermal noise leading asymp-totics of pair and high-order correlators of the velocity field are found for finite times and large distances. It is shown that the intermittency takes place: some correlators are much larger than their reducible parts. Intermittency implies strong non-Gaus...

Optimal control problems (OCP) for Burgers equation are important for the development of numerical methods for optimal control of more complicated models in fluid dynamics such as Navier-Stokes equations. In this work, we analyze variant preconditioners for the saddle point problem arising from boundary control of unsteady Burgers equation. As for a solution approach for the discretization of t...