In this paper, a numerical method is developed to approximate the soliton solutions of some nonlinear wave equations in terms of the Jacobi polynomials. Wave are very important phenomena in dispersion, dissipation, diffusion, reaction, and convection. Using the wave variable converts these nonlinear equations to the nonlinear ODE equations. Then, the operational Collocation method based on Jacobi polynomials as bases is applied to approximate the solution of ODE equation resulted. In addition, the intervals of the solution will be extended using an rational exponential approximation (REA). The KdV, Boussinesq, and Kaup–Kuperschmidt equations are studied as the test examples. Finally, numerical computation of the conservation values shows the effectiveness and stability of the proposed method.
Sadri, Khadijeh and Ebrahimi, Hamideh
Numerical Study of Soliton Solutions of KdV, Boussinesq, and Kaup-Kuperschmidt Equations Based on Jacobi Polynomials,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 12,
1, Article 11.
Available at: https://digitalcommons.pvamu.edu/aam/vol12/iss1/11