Fractional Consistent Riccati Expansion Method and Soliton-Cnoidal Solutions for the Time-Fractional Extended Shallow Water Wave Equation in (2 + 1)-Dimension
Year: 2024
Type: article
Abstract: In this work, a fractional consistent Riccati expansion (FCRE) method is proposed to seek soliton and soliton-cnoidal solutions for fractional nonlinear evolutional equations. The method is illustrated by the time-fractional extended shallow water wave equation in the (2 + 1)-dimension, which includes a lot of KdV-type equations as particular cases, such as the KdV equation, potential KdV equation, Boiti–Leon–Manna–Pempinelli (BLMP) equation, and so on. A rich variety of exact solutions, including soliton solutions, soliton-cnoidal solutions, and three-wave interaction solutions, have been obtained. Comparing with the fractional sub-equation method, G′/G-expansion method, and exp-function method, the proposed method gives new results. The method presented here can also be applied to other fractional nonlinear evolutional equations.
Source: Fractal and Fractional
Authors: Lihua Zhang, Bo Shen, Meizhi Jia, Zhenli Wang, Gangwei Wang
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,069
OpenAlex ID: W4403389678