A number of nonlinear phenomena in many branches of sciences such as physical [6], chemical, economical [20] and biological processes [15,14] are described by the interplay of reaction and diffusion or by the interaction between convection and diffusion. One of the well-known partial differential equations (PDEs) which governs a wide variety of them is Burgers equation, which provides the simpl...

We investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg–Landau equation, we establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, we show that the viscous shock profil...

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.

In this paper, we consider the Burgers’ equation with a time delay. By using the Liapunov function method, we show that the delayed Burgers’ equation is exponentially stable if the delay parameter is sufficiently small. We also give an explicit estimate of the delay parameter in term of the viscosity and the initial condition, which indicates that the delay parameter tends to zero if the initia...

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 ...