Travelling wave solutions in a model of the helix polypeptide chains

By using the theory of bifucations of dynamical systems to a model of the helix polypeptide chains, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. In some simple conditions, exact explicit and implicit solution formulas are listed.