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...

Keywords: Compact schemes Finite difference method Burgers' equation Low-storage Runge–Kutta scheme a b s t r a c t A numerical solution of the one-dimensional Burgers' equation is obtained using a sixth-order compact finite difference method. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge–Kutt...

We explore a connection of the forced Burgers equation with the Schrödinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In general, the usage of a continuity equation ∂ t ρ = −∇(vρ), wh...

We give an alternative derivation of two Painlevé hierarchies. This is done by constructing generalized scaling reductions of the Korteweg-de Vries and dispersive water wave hierarchies. We also construct a generalized scaling reduction of Burgers hierarchy. Corresponding author: P. R. Gordoa. Tel: +34 91 4888243; Fax: +34 91 488 7338; email: [email protected]