Abstract
In this paper, we study the nonlinear wave solutions of thegeneralized $b$-equation involving two parameters $b$ and $k$. Let$c$ be constant wave speed, $c_5=$$\frac{1}{2}(1+b-\sqrt{(1+b)(1+b-8k)})$,$c_6=\frac{1}{2}(1+b+\sqrt{(1+b)(1+b-8k)})$. We obtainthe following results: 1. If $-\infty 2. If $-\infty 3. If $k=\frac{1+b}{8}$ and $c=\frac{b+1}{2}$, then there aretwo types of explicit nonlinear wave solutions, fractionalpeakon wave solution and fractional blow-up solution.Not only is the existence of these solutions shown, but theirconcrete expressions are presented. We also reveal the relationships amongthese solutions. Besides, the correctness of these solutionsis tested by using the software Mathematica.
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
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.