On generating linear and nonlinear integrable systems with variable coefficients
On generating linear and nonlinear integrable systems with variable coefficients
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关于生成变系数线性和非线性可积系统
DOI：
10.1016/j.amc.2014.07.030
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发表时间：
2014-10
影响因子：
4
通讯作者：
Wang Guangming
中科院分区：
文献类型：
--
作者：
Zhang Yufeng;Zhao Zhonglong;Wang Guangming
Under an isospectral Lax pair, a new integrable hierarchy of evolution equations is obtained by starting from a given Lie algebra T, which can be reduce to a new coupled integrable equation similar to the long wave equation, but it is not the standard long wave equation. By making use of an enlarged Lie algebra T 1 of the Lie algebra T, we obtain a type of equation hierarchy (called a linear hierarchy). The corresponding Hamiltonian structure of the equation hierarchy is derived from the variational identity. As we all know that nonlinear equations with variable coefficients can be used to describe some real phenomena in physical and engineering fields. It is an interesting and important topic to consider how to generate variable-coefficient nonlinear integrable equations from the mathematical viewpoint. In the paper, we construct another enlarged Lie algebra T 2 of the Lie algebra T for which an integrable hierarchy (called the nonlinear hierarchy) of nonlinear integrable equations with variable coefficients is obtained. Furthermore, the Hamiltonian structure of the integrable hierarchy is produced by using the variational identity again. As long as the linear hierarchy and the nonlinear hierarchy are derived, following their reductions, some linear and nonlinear evolution equations with variable coefficients are obtained, respectively. The corresponding Hamiltonian structures of such reduced equations with variable coefficients are followed to present.
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影响因子：
0.3
作者：
W. Ma
通讯作者：
W. Ma
影响因子：
1.6
作者：
Z. Qiao
通讯作者：
Z. Qiao
影响因子：
8.6
作者：
V. Serkin;A. Hasegawa
通讯作者：
V. Serkin;A. Hasegawa
影响因子：
3.1
作者：
Zhang Yu-feng
通讯作者：
Zhang Yu-feng
DOI：
10.1007/978-1-4612-1282-9
发表时间：
2000-02
期刊：
--
影响因子：
--
作者：
M. Zamir
通讯作者：
M. Zamir