Abstract
The coupled Boussinesq equation (CBE) acts a key role in modeling the shallow water waves of two-layer fluid flow. However, it becomes powerless for the nonsmooth boundary. So, a fractal modification of the CBE is suggested in this paper. Aided by the semi-inverse method, we successfully construct its fractal generalized variational principle. In addition, three recent techniques, namely, the Sardar-subequation method, He’s frequency formulation method and subequation method, combined with the two-scale fractal dimension transform, are utilized to find abundant wave solutions. By these methods, various solutions expressed by the generalized hyperbolic functions, generalized trigonometric functions, hyperbolic functions and cosine function are obtained. With the aid of the mathematical software, the three-dimensional contours and two-dimensional curves are plotted to present the dynamic behaviors of the solutions. The results in this paper demonstrate that the proposed methods are powerful and effective to construct the traveling wave solutions of the fractal nonlinear evolution equations.
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.