论文信息 - Numerical doubly periodic solution of the KdV equation with the initial condition via the decomposition method

Numerical doubly periodic solution of the KdV equation with the initial condition via the decomposition method

In this paper, a scheme is extended to study numerical doubly periodic solutions of the Kortweg-de Vries (KdV) equation with initial conditions using the Adomian decomposition method. As a result, we obtain the numerical doubly periodic solutions of the KdV equation with initial conditions. The numerical doubly periodic solution is compared with the exact doubly periodic solution. Moreover we analyze the absolute error and relative error between them, and also give the contour and density plots of the numerical doubly periodic solutions with two different moduli: m=15,78.

Zhenya Yan

[1] J. Rogers. Chaos , 1876 .

[2] Zhenya Yan,et al. New families of solitons with compact support for Boussinesq-like B(m,n) equations with fully nonlinear dispersion , 2002 .

[3] Salah M. El-Sayed,et al. Numerical soliton-like solutions of the potential Kadomtsev–Petviashvili equation by the decomposition method , 2003 .

[4] Abdul-Majid Wazwaz,et al. Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method , 2001 .

[5] R. Hirota. Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[6] P. Stevenhagen,et al. ELLIPTIC FUNCTIONS , 2022 .

[7] Abdul-Majid Wazwaz,et al. The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model , 2000, Appl. Math. Comput..

[8] Abdul-Majid Wazwaz,et al. A computational approach to soliton solutions of the Kadomtsev-Petviashvili equation , 2001, Appl. Math. Comput..

[9] P. Clarkson,et al. Solitons, Nonlinear Evolution Equations and Inverse Scattering: References , 1991 .

[10] M. Ablowitz,et al. Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[11] G. Adomian. A review of the decomposition method in applied mathematics , 1988 .

[12] G. Adomian,et al. Solving frontier problems of physics : the decomposition methoc [i.e. method] , 1994 .

[13] Andrew G. Glen,et al. APPL , 2001 .