Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...

Abstract: In this paper, the Exp-function method with the aid of symbolic computational system is used to obtain generalized solitary solutions and periodic solutions of the MKdV equation, Burgers’ equation in one and two dimensional with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving othe...

Abstract In the proposed work, an improvised collocation technique with cubic B-spline as basis functions is applied to obtain numerical solution of non-linear generalized Burgers’–Huxley equation, which has application in soliton theory. this technique, posteriori corrections are made interpolant and its higher-order derivatives, leads enhancement order convergence spatial domain. The temporal...

Abstract. A time-dependent Hermite-Galerkin spectral method (THGSM) is investigated in this paper for the nonlinear convection-diffusion equations in the unbounded domains. The timedependent scaling factor and translating factor are introduced in the definition of the generalized Hermite functions (GHF). As a consequence, the THGSM based on these GHF has many advantages, not only in theorethica...

There are presented the investigations in the framework of pseudoanalysis semirings whose operations are generated with functions of one variable. Based on the operations with generators there was developed a theory of generalized functions in analogy to the Mikusiński’s operators, which enables the construction of a generalized solution of the Burgers equation. There are considered extensions ...

Abstract: A new periodic wave solution in terms of Riemann theta functions to the elliptic equation is presented, then by using this solution and the improved generalized F-expansion method, some exact solutions in terms of Riemann theta functions to the KdV-Burgers-Kuramoto(KBK) equation are obtained with the aid of Mathematica, their properties and profiles are displayed in their figures. To ...

The conditions for a generalized Burgers equation which a priori involves nine arbitrary functions of one, or two variables to allow an infinite dimensional symmetry algebra are determined. Though this algebra can involve up to two arbitrary functions of time, it does not allow a Virasoro algebra. This result confirms that variable coefficient generalizations of a non-integrable equation should...

Analytic continuation of viscous shock solution for the generalized Burgers equation with polynomial nonlinear source term is investigated. We show that a pertubated wave recovers its analyticity in the space variable in the strip limited by the first pair of conjugate poles of the wave.

The modified simple equation method is employed to find the exact traveling wave solutions involving parameters for nonlinear evolution equations namely, a diffusive predator-prey system, the Bogoyavlenskii equation, the generalized Fisher equation and the Burgers-Huxley equation. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wa...

Submitted: Mar 2, 2013; Accepted: Apr 10, 2013; Published: Jun 10, 2013 Abstract: In this article, we present a variant approach of the generalized and improved (G'/G)–expansion method and construct some new exact traveling wave solutions with free parameters of the nonlinear evolution equations, via the Painleve integrable Burgers equation, the Boiti-Leon-Pempinelle equation and the Pochhammer...