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SOLVING THE KORTEWEG-DE VRIES EQUATION BY A NUMERICAL METHOD
Keywords:
KdV, SBA methodDOI:
https://doi.org/10.17654/0972087126003Abstract
In one of our articles published in 2017 [12], we used the SBA method to show its simplicity in solving the Schrödinger equation. In this paper, we propose a solution to the Korteweg-de Vries (KdV) equation using the SBA method.
Received: April 17, 2025
Accepted: May 5, 2025
References
[1] B. Abbo, Nouvel algorithm numérique de résolution des équations différentielles ordinaires (EDO) et des équations aux dérivées partielles (EDP) non linéaires, Thèse de Doctorat unique, Université de Ouagadougou, 2007.
[2] B. Abbo, O. So, G. Barro and B. Some, A new numerical algorithm for solving nonlinear partial differential equations with initial and boundary conditions, Far East J. Appl. Math. 28(1) (2007), 37-52.
[3] G. Adomian, A review the decomposition method in applied mathematics, J. Math. Anal. Appl. 135 (1988), 501-544.
[4] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Pub., 1994.
[5] Snehashish Chakraverty, Nisha Rani Mahato, Perumandla Karunakar and Tharasi Dilleswar Rao, Advanced Numerical and Semi-analytical Methods for Differential Equations, John Wiley and Sons, Inc., 2019.
[6] C. S. Gardner and G. K. Morikawa, The effect of temperature on the width of a small-amplitude, solitary wave in a collision-free plasma, Comm. Pure Appl. Math. 18 (1965), 35-49.
[7] J. E. Lidsey, Cosmology and the Korteweg-de Vries equation, Phys. Rev. D. 86(12) (2012).
[8] H. D. Wahlquist and F. B. Estabrook, Bäcklund transformation for solutions of the Korteweg-de Vries equation, Phys. Rev. Lett. 31 (1973), 1386-1390.
[9] H. Washimi and T. Taniuti, Propagation of ion-acoustic solitary waves of small amplitude, Phys. Rev. Lett. 17 (1966), 996-998.
[10] N. J. Zabusky, A synergetic approach to problems of nonlinear dispersive wave propagation and interaction, Nonlinear Partial Differential Equations 1967, 223-258.
[11] V. E. Zakharov, The Inverse Scattering Method, Springer, 1980.
[12] Gérard Zongo, Ousséni So, Geneviève Barro, Youssouf Paré and Blaise Somé, A comparison of Adomian’s method and SBA method on the nonlinear Schrödinger’s equation, Far East Journal of Dynamical Systems 29(4) (2017), 149-161.
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