Exact solutions of a generalized Boussinesq equation

Abstract

We analyze a generalized Boussinesq equation using the theory of symmetry reductions of partial differential equations. The Lie symmetry group analysis of this equation shows that the equation has only a two-parameter point symmetry group corresponding to traveling-wave solutions. To obtain exact solutions, we use two procedures: a direct method and the G /G-expansion method. We express the traveling-wave solutions in terms of hyperbolic, trigonometric, and rational functions.

Propagation of elastic solitons in chains of pre-deformed beams

“…Remarkably, it has been shown that the Boussinesq equation admits the solitary wave solution [37,38]…”

Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation

“…where h(z) = sn(z, ) is a solution of (21), and taking into account that sn(z, ) = tanh(z), we obtain that for µ = and ω =…”

“…A great progress has being made in the development of methods and their applications for nding solitary traveling-wave solutions of nonlinear evolution equations. Many solutions of nonlinear partial di erential equations have been found by one or other of these methods [21][22][23][24].…”

Symmetries, Traveling Wave Solutions, and Conservation Laws of a(3+1)-Dimensional Boussinesq Equation

“…Wazwaz [5] employed a combination of Hirota's method and Hereman's method to formally study (3) and derived two soliton solutions of (3). Some other work concerning symmetries and exact solutions of some Boussinesq equations can be seen in [9][10][11][12].…”