Fermionic covariant prolongation structure theory for supernonlinear evolution equation
Fermionic covariant prolongation structure theory for supernonlinear evolution equation
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DOI：
10.1063/1.3474917
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发表时间：
2010-09
影响因子：
1.3
通讯作者：
Jipeng Cheng;Shi-kun Wang;Ke Wu;Wei-zhong Zhao
中科院分区：
文献类型：
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作者：
Jipeng Cheng;Shi-kun Wang;Ke Wu;Wei-zhong Zhao
我们研究了超主丛及其相关的超丛。构造了超纤维丛上的超（非线性）联络。然后利用联系理论建立了超非线性发展方程的费米子协变延拓结构理论。在这种几何理论中，给出了决定延拓结构的费米子协变基本方程。作为一个例子，在此费米协变延拓结构理论框架下分析了超非线性薛定谔方程。我们得到了它的Lax对和Backlund变换。
We investigate the superprincipal bundle and its associated superbundle. The super(nonlinear)connection on the superfiber bundle is constructed. Then by means of the connection theory, we establish the fermionic covariant prolongation structure theory of the supernonlinear evolution equation. In this geometry theory, the fermionic covariant fundamental equations determining the prolongation structure are presented. As an example, the supernonlinear Schrodinger equation is analyzed in the framework of this fermionic covariant prolongation structure theory. We obtain its Lax pairs and Backlund transformation.