The sine–cosine and the tanh methods: Reliable tools for analytic treatment of nonlinear dispersive equations

The sine–cosine method and the tanh method are used for analytic treatment of nonlinear dispersive equations. Nonlinear variants of Boussinesq equation are used as vehicles to show the strength of these methods. Solutions of distinct physical structures: solitons, compactons, solitary patterns solutions and periodic solutions are formally derived. The results show that the change in physical structures of the obtained solutions depends mainly on exponents and on the coefficients of the derivatives involved.