A study of Kudryashov equation and its chaotic behaviors

The main target of this paper is to solve the Kudryashov equation (KE) and present the chaotic behaviors of the equation. Firstly, we take the traveling wave transformation to the original equation and obtain the corresponding dynamic system as well as the Hamiltonian. Then the qualitative analysis is conducted to establish the existence of periodic solutions and solitons of the equation. In order to confirm our findings, we construct the corresponding exact solutions and obtain a new type solution, which makes our conclusion more complete. In particular, we consider the perturbed form of KE and analyze the chaotic behaviors of KE in detail. As far as we know, it is the first time that the chaotic behaviors of KE are presented. Our results enrich the study of the KE equation and propose a new direction for the following study of this equation.