Theoretical and Mathematical Physics

, Volume 160, Issue 1, pp 894-904

First online:

Exact solutions of a generalized Boussinesq equation

  • M. S. BruzónAffiliated withDepartamento de Matemáticas, Universidad de Cádiz Email author 

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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.


partial differential equation symmetry solution