Version 1
: Received: 1 August 2024 / Approved: 2 August 2024 / Online: 2 August 2024 (06:04:29 CEST)
How to cite:
Zhang, L.; Zheng, Z.; Shen, B.; Wang, G.; Wang, Z. Interaction Solutions for the Fractional KdVSKR Equations in (1+1)-Dimension and (2+1)-Dimension. Preprints2024, 2024080130. https://doi.org/10.20944/preprints202408.0130.v1
Zhang, L.; Zheng, Z.; Shen, B.; Wang, G.; Wang, Z. Interaction Solutions for the Fractional KdVSKR Equations in (1+1)-Dimension and (2+1)-Dimension. Preprints 2024, 2024080130. https://doi.org/10.20944/preprints202408.0130.v1
Zhang, L.; Zheng, Z.; Shen, B.; Wang, G.; Wang, Z. Interaction Solutions for the Fractional KdVSKR Equations in (1+1)-Dimension and (2+1)-Dimension. Preprints2024, 2024080130. https://doi.org/10.20944/preprints202408.0130.v1
APA Style
Zhang, L., Zheng, Z., Shen, B., Wang, G., & Wang, Z. (2024). Interaction Solutions for the Fractional KdVSKR Equations in (1+1)-Dimension and (2+1)-Dimension. Preprints. https://doi.org/10.20944/preprints202408.0130.v1
Chicago/Turabian Style
Zhang, L., Gangwei Wang and Zhenli Wang. 2024 "Interaction Solutions for the Fractional KdVSKR Equations in (1+1)-Dimension and (2+1)-Dimension" Preprints. https://doi.org/10.20944/preprints202408.0130.v1
Abstract
In this paper, we extend the KdVSKR equations in (1+1)-dimension and (2+1)-dimension to fractional KdVSKR equations with modified Riemann-Liouville derivative. The (2+1)-dimensional KdVSKR equation, which is a recent extension of (1+1)-dimensional KdVSKR equation, can model the resonances of solitons in shallow water. By means of the Hirota bilinear method, finite symmetry group method and consistent Riccati expansion method, many new interaction solutions have been derived. Soliton-cnoidal interaction solution of the (1+1)-dimensional fractional KdVSKR equation has been derived for the first time. For the (2+1)-dimensional frac-tional KdVSKR equation, two-wave interaction solutions and three-wave interaction solutions, including dark-soliton-sine interaction solution, bright-soliton-elliptic interaction solution, and lump-hyperbolic-sine interaction solution, have been derived. Impact of the fractional order on the shapes of these solutions has been illustrated by figures. Three-wave interaction solutions of fractional systems have not been reported in the existing references. The research idea in this paper can be applied to other fractional differential equations.
Copyright:
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