某类非线性常微分方程解的形式
The Form of Solution for a Class of Nonlinear Ordinary Differential Equations
摘要: 本论文主要应用F展开法求解某类非线性常微分方程的精确解。首先利用相应自变量变换，再通过齐次平衡法的思想确定方程的某种解的形式，应用数学软件Maple进行求解，再结合相应的Riccati方程的解的表达式，得到了该类非线性常微分方程的精确解的表达形式。
Abstract:
In this paper, the exact solution of a class of nonlinear ordinary differential equations is solved by using the F-expansion method. Firstly, by using variable transformation, and through the idea of the homogeneous balance method, some forms of solution are given. By application of mathematical software Maple, some solutions are solved combined with the solution of Riccati equation. And forms of the exact solutions of nonlinear ordinary differential equations are obtained.
参考文献
|
[1]
|
Yang, L., Zhu, Z.G. and Wang, Y.H. (1999) Exact Solutions of Nonlinear Equations. Physics Letters A, 260, 55-59.
https://doi.org/10.1016/S0375-9601(99)00482-X
|
|
[2]
|
Cao, D.B. (2002) New Exact Solutions for a Class of Nonlinear Coupled Differential Equations. Physics Letters A, 296, 27-33.
https://doi.org/10.1016/S0375-9601(02)00151-2
|
|
[3]
|
Ruan, H.Y. and Chen, Y.X. (2003) Soliton Interactions of Integrable Models. Chaos, Solitons and Fractals, 17, 929- 939.
https://doi.org/10.1016/S0960-0779(02)00576-3
|
|
[4]
|
何宝钢, 徐昌智, 张解放. (2+1)维非线性KdV方程的新孤子结构[J]. 物理学报, 2005, 54(12): 5525-5529.
|
|
[5]
|
刘常福. Davey-Stewartson I方程的精确波类解[D]: [硕士学位论文]. 云南: 云南大学, 2006.
|
|
[6]
|
Wang, M.L. (1995) Solitary Wave Solutions for Variant Boussinesq Equations. Physics Letters A, 199, 169-172.
https://doi.org/10.1016/0375-9601(95)00092-H
|
|
[7]
|
Swift, J.B. and Hohenberg, P.C. (1977) Hydrodynamic Fluctuations at the Convective Instability. Physical Review A, 15, 319-328.
https://doi.org/10.1103/PhysRevA.15.319
|