The Burgers equation with linear damping has been subjected to Lie's group theoretic method of infinitesimal transformation to derive its solutions. To the best of our knowledge, we are the first to obtain a new similarity variable for an equation of the Burgers type and therefore provide new solutions.

In this paper, we discuss a link of Itô’s stochastic differential equations to nonlinear partial differential equations of Burgers type. Under certain conditions, we derive a generalised Burgers equation from a stochastic differential equation. We also give some economic interpretation of our result as well as the relevant conditions. Mathematics Subject Classification (2000): 60H10, 35K58, 91G99.

In this paper, the control problem of the forced Burgers equation: ∂u ∂t = ν ∂2u ∂x2 − u ∂u ∂x +mu+ f(x), 0 < x < 2π, t > 0 subject to Neumann boundary conditions: ∂u ∂x (0, t) = ũ1(t), ∂u ∂x (2π, t) = ũ2(t) t > 0. and the initial condition: u(x, 0) = u0(x), x ∈ (0, 2π) t > 0, where ν is a positive constant, the parameter m ∈ IR, and ũ1(t), ũ2(t) are two control inputs is considered. We show th...

In this paper, numerical solution of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is obtained by using the mesh-free method based on the collocation method with radial basis functions (RBFs). Stability analysis of the method is discussed. The method is applied to several examples and accuracy of the method is tested in terms of $L_2$ and $L_infty$ error norms.

In this paper, a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term -k2x + f(t), k is an element of R is presented. Two methods existing for the case K=0 are adapted and generalized using variable and functional transformations, valid for all values of space and time. The emergence of a Fokker-Planck equation in the method allows the establishme...

A Bäcklund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat equation is resolved by the Fourier transformation method, substituting various solutions of the initial problem of the heat equation will yield solutions of the in...