Bifurcations of travelling wave solutions for two generalized Boussinesq systems (Q2519320)

The paper concerns two generalized parametric Boussinesq systems, already considered by \textit{Y. Li, W.-X. Ma} and \textit{J. E. Zhang} in [Phys. Lett., A 275, No. 1--2, 60--66 (2000; Zbl 1115.35329); \textit{Y. A. Li}, J. Dyn. Differ. Equations 11, No. 4, 625--669 (1999; Zbl 0941.35078)]. The existence of solitary waves, solitary cusp waves, kink and anti-kink waves is discussed. Moreover, the existence of many uncountably infinite periodic wave solutions is obtained. Finally, the parametric representations of the bounded travelling wave solutions are determined. The author uses a dynamical system approach describing the dynamical behavior of the travelling wave solutions, depending on the parameters of the systems.