Abstract
In this paper, we focus on studying the exact solitary wave solutions and periodic wave solutions of the generalized modified Boussinesq equation utt−δuttxx−(a1u+a2u2+a3u3)xx=0, as well as the evolution relationship between these solutions. Detailed qualitative analysis is conducted on traveling wave solutions of this equation, and global phase portraits in various parameter conditions are proposed. Various significant results about the existence of both solutions, including three forms of solitary wave solutions and four exact bounded periodic wave solutions in different conditions are obtained. Then, we further discuss the relationship between energy of Hamiltonian system corresponding to this equation and the periodic wave solutions and solitary wave solutions. It is concluded that the essential reason of periodic wave solutions and solitary wave solutions is the different values for the energy of Hamiltonian system corresponding to this equation. In addition, the limited relations of periodic wave solutions and solitary wave solutions with the energy of Hamiltonian system are proposed, and the schematic diagram of evolution from periodic wave solutions to solitary wave solutions is drawn.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
