Abstract
The Lie group method stands as a significant, powerful, and straightforward mathematical tool for discovering precise invariant solutions and traveling wave solutions in prevalent nonlinear evolution equations across engineering, applied mathematics, and physics. The interplay of dispersive effects arising from material microstructure, combined with nonlinearities, results in the formation of solitary waves. In this article, we apply the Lie group method to derive invariant and comprehensive traveling wave solutions for the strain wave equation in microstructured solids. This yields a diverse array of exact solutions, including traveling wave solutions, solitons, shock waves, periodic, singular, and rational solutions, all of which bear potential significance in various engineering applications.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.