Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended G G ′       -expansion method, substituting the solutions obtained into the cor...

The Burgers’ equation first appeared in the paper by Bateman [3], who mentioned two of the essentially steady solutions. Due to extensive works of Burgers [4] involving the Burgers’ equation especially as a mathematical model for the turbulence, it is known as Burgers’ equation. The equation is used as a model in fields as wide as heat conduction [5], gas dynamics [13], shock waves [4], longitu...

In this paper, we consider a generalized BenjaminBona-Mahony-Burgers equation. Classical symmetries of this equation are considered. The functional forms, for which the BBMB equation can be reduced to ordinary differential equations by classical Lie symmetries, are obtained. A catalogue of symmetry reductions and a catalogue of exact solutions are given. A set of new solitons, kinks, antikinks,...

The exact traveling wave solutions of the nonlinear variable coefficients Burgers-Fisher equation and the generalized Gardner equation with forced terms can be found in this article using the generalized ( ′ G )-expansion method. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. When these parameters are taken special values, the solitary wave ...

We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equation. The planar systems with degenerate equilibrium arising after traveling transformation are investigated. By finding certain positive definite Lyapunov functions neighborhood singular points and Hopf bifurcation points, number possible limit cycles corresponding is determined. existence equation...