By the Cole-Hopf transformation, with any linear evolution equation in 1 + 1 dimensions a generalized Burgers equation is associated. We describe local conservation laws of these equations. It turns out that any generalized Burgers equation has only one conservation law, while a linear evolution equation with constant coefficients has an infinite number of (x, t)independent conservation laws if...

The equal width wave (EW) equation is a model partial differential equation for the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes. The EW-Burgers equation models the propagation of nonlinear and dispersive waves with certain dissipative effects. In this work, we derive exact solitary wave solutions for the general form of the EW equation and the gen...

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

in this paper, modified simple equation method has been applied to ob-tain generalized solutions of burgers, huxley equations and combined forms of these equations. the new exact solutions of these equations have been obtained. it has been shown that the proposed method provides a very effective, and powerful mathematical tool for solving nonlinear partial differential equations.

Rudie P. J. Kunnen1†, Richard J. A. M. Stevens2, Jim Overkamp1, Chao Sun2, GertJan F. van Heijst1 and Herman J. H. Clercx1,3 1 Department of Physics and J.M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands 2 Department of Science and Technology and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, ...

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...

Salas, Gomez and Heranańdez [A.Y. Salas S., C.A. Gomez S., J.E.C Hernańdez, New abundant solutions for tha Burgers equation, Computers and Mathematics with Applications 58 (2009) 514 -520] presented 70 ”new exact solutions” of a ”generalized version” of the Burgers equation. In this comment we show that all 70 solutions by these authors are not new and cannot be new. PACS: 02.30.Jr Ordinary dif...