Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system. (February 2020)

• Record Type: Journal Article
• Authors: Ali, Ahmad T.; Khater, Mostafa M.A.; Attia, Raghda A.M.; Abdel-Aty, Abdel-Haleem; Lu, Dianchen
• Is Part Of: Chaos, solitons and fractals. Volume 131(2020)
• Publication Date: 2020-02
• Subjects: The generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation -- The modified Khater method -- B-spline scheme -- Computational solution -- Approximate solutions; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.109473
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: This research paper investigates the analytical and numerical solutions of the generalized formula of Hirota-Satsuma coupled KdV system which is also known as the generalized KdV equation that is derived by R. Hirota and J. Satsuma. The modified Khater method and B-spline scheme are used to earn abundant of computational and approximate solutions on this model. This equation characterizes an interaction of two long undulations with diverse dispersion kinsmen. The comparison between our obtained computational and numerical solutions to clarify the convergence of solutions is explained and discussed. For more explanation of the model's physical properties, some of the obtained solutions are sketched in different types, and the comparison between the computational and numerical solutions are explained by showing the values of absolute error between them. The performance of both used method is effective, powerful, and shows its ability to apply to many nonlinear evolution equations.