In this paper, we construct an analytical solution of the coupled Burgers’ equation, using homotopy analysis method, which is a semi-analytical approximate obtained by method convergent for different values convergence control parameter ℏ, optimal value ℏ corresponding with minimum error to be determined residual. The results present are compared other solutions numerical methods.

Existence, uniqueness and regularity of the global weak solution to the Burgers equation with a reaction term is shown when the reaction term is given as a time independent point source and produces heat constantly. An explicit solution is obtained and used to show the long time asymptotic convergence of the solution to a steady state. For the heat equation case without any convection the solut...

In this paper, a nonlinear dispersive wave equation Burgers-Poisson (BP) equation is considered. We present a classification of group invariant solutions for the BP equation by using classical Lie method. Mathematics Subject Classification; 35Q53

We complete the program outlined in the paper of the author with A. Migdal and sum up exactly all the fluctuations around the instanton solution of the randomly large scale driven Burgers equation. The probability distribution coincides with the one conjectured by A. Polyakov within the applicability of the perturbation theory. In paper [1] we computed the probability distribution P (δu, r) of ...

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,...

In many application areas ranging from shock waves to acoustics, we encounter the same partial differential equation known as the Burgers’ equation. The fact that the same equation appears in different application domains, with different physics, makes us conjecture that it can be derived from the fundamental principles. Indeed, in this paper, we show that this equation can be uniquely determin...

It has been known for a while that a nonlinear equation driven by singular noise must be interpreted in the re-normalized, or Wick, form. For the stochastic Burgers equation, Wick nonlinearity forces the solution to be a generalized process no matter how regular the random perturbation is, whence the curse. On the other hand, certain multiplicative random perturbations of the deterministic Burg...

We study certain similarity solutions of the Benjamin-Ono-Burgers (BOB) equation and their role in the asymptotic behavior of the general solution. For small initial data in L 1 (R) we prove that a solution of the BOB equation exists in BC(R + ; L 1 (R)) and depends continuously on its initial data. Results about existence, uniqueness, regularity, and spatial asymptotics of solutions of a simil...

A new differential quadrature method based on quartic B-spline functions is introduced. The weighting coefficients are determined via a semi-explicit algorithm containing an algebraic equation system with four-band coefficient matrix. In order to validate the proposed method, the Burgers’ Equation is selected as test problem. The shock wave and the sinusoidal disturbance solutions of the Burger...

where: x is position in one or more spatial dimensions; u(x, t) is some scalar or vector field, such as fluid velocity and pressure; L is a dissipative linear operator, such as ∇; f(u) includes other autonomous terms representing nonlinear advection, reaction, etc.; and q(u, t) is some time dependent control or possibly stochastic forcing [22]. Among many physically relevant examples are Burger...