Bifurcations of traveling wave solutions for a class of the nonlinear equations

The dynamical behavior of traveling wave solutions in a class of the nonlinear k(n, n) equations with negative exponents is studied by using the theory of bifurcations of dynamical systems. As a result, the dynamical behavior of different physical structure: solitary patterns, solitons, periodic, kink and anti-kink wave solutions are obtained. When parameters are varied, the conditions under which the above solutions appear are also shown. In addition, some exact explicit solutions are given.