Bifurcations of travelling wave solutions in a model of the hydrogen-bonded systems Jianwei Shen a,c, * , Jibin Li b , Wei Xu a a Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR China b School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650093, PR China c Department of Mathematics, Xuchang University, Xuchang, Henan 461000, PR China Abstract By using the theory of bifucations of dynamical systems to a model of the Hydrogen- bonded systems, 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 parametric conditions, exact explicit and implicit solution formulas are listed. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Solitary travelling wave solution; Periodic travelling wave solution; Kink and anti-kink wave solutions; Smoothness of waves 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.01.058 * Corresponding author. Address: Department of Applied Mathematics, Northwestern Poly- technical University, XiÕan, Shaanxi 710072, PR China. E-mail addresses: jwshen@mail.edu.cn (J. Shen), jibinli@ynu.edu.cn (J. Li). Applied Mathematics and Computation 171 (2005) 242–271 www.elsevier.com/locate/amc