A Spiral Model Of The Polypeptide Chain Traveling Wave Solutions

By using the theory of bifurcations 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.In chapter 1, the paper introduce the corresponding model and results, In chapter 2, the paper discuss bifurcations of phase portraits of (1.5) when U( ) given by (1.2). In chapter 4, the paper discuss bifurcations of phase portraits of (1.5) when U( ) given by (1.3). In chapter 3 and chapter 5, the paper consider the existence of solitary, kink traveling wave and periodic traveling wave solutions of (1.1) and give some explicit exact solution formulas.