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用变量分离常微分方程方法求Boussinesq-double sine-Gordon 和Boussinesq-double sinh-Gordon方程的行波解

日期:2018年01月15日 编辑: 作者:无忧论文网 点击次数:1660
论文价格:50元/篇 论文编号:lw200906261401337228 论文字数:2838 所属栏目:英语论文翻译
论文地区:中国 论文语种:中文 论文用途:文献翻译 Literature Translation
be found in [9,2,13,14]. 2. The variable separated ODE method As stated before, this method was developed by Sirendaoreji et al. [9]. We first unite the independent variables x and t into one wave variable ξ = x − ct to carry out a PDE into an equivalent ODE. The method depends mainly on assuming that u(ξ) satisfies an additional variable separated ODE given byu = du dξ = G(u), (10) where G(u) is a suitable function of sine, cosine, hyperbolic sine, hyperbolic cosine. Differentiating (10) and equating the coefficients of like terms of the resulting equation with the ODE reduced from the PDE yields a system of algebraic equations that can be solved to determine the unknown parameters. It is worth noting that the variable separated ODE (10) can be solved easily by using the method of separation of variables. It should be noted that the selection of G(u) can be performed in more than one choice as will be seen later.

摘 要 :Boussinesq-double sine-Gordon (B-sine-Gordon)方程,Boussinesq- double sinh-Gordon(B-sinh-Gordon)方程和 Boussinesq-Liouville(BL)方程的行波解被推导出来了。该方法主要在于对常微分方程用变量可分离的方法。它拥有独特的物理结构,能为每个方程得到两类不同的精确的孤立波解。 © 2006 IMACS。由 Elsevier B 出版,保留所有权利。
1.引言
2.变量分离常微分方程方法
3.Boussinesq-double sine-Gordon 等式
4.Boussinesq-double sinh-Gordon 等式
5. Boussinesq-Liouville 方程I
6. Boussinesq-Liouville 方程II
7.讨论