The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley eq...

In this work, the G G        -expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the G G        -expansion method provides not only more general forms of solutions but als...

In this paper, we deal with both nonviscous and viscous Burgers type equations on a bounded interval. We study the global exact controllability of these equations when we have three controls: one control is the right member of the equation and is constant with respect to the space variable, the two others are the boundary values. In a first time, we are interested in nonviscous Burgers type equ...

We consider a simplified model of vertical non-static groundwater flow, resulting in a Burgers’ diffusive equation extended with a third order term with mixed derivatives in space and time. This model is motivated by previous work on the existence of travelling wave solutions on a more general model. We investigate stability of travelling wave solutions of the simplified model, for which we fir...

A new stochastic cellular automaton (CA) model of traffic flow, which includes slow-to-start effects and a driver’s perspective, is proposed by extending the Burgers CA and the Nagel-Schreckenberg CA model. The flowdensity relation of this model shows multiple metastable branches near the transition density from free to congested traffic, which form a wide scattering area in the fundamental dia...

By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-BonaMahony-Burgers (shortly BBMB) equations in its bilinear form. Keywords—Benjamin-Bona-Mahony-Burgers equations, Hirota’s bilinear form, Three-wave method.

Lie point symmetries of time-fractional potential Burgers' equation are presented. Using these symmetries fractional potential Burgers' equation has been transformed into an ordinary differential equation of fractional order corresponding to the Erdélyi-Kober fractional derivative. Further, an analytic solution is furnished by means of the invariant subspace method. AMS subject classifications:...