首页 | 本学科首页   官方微博 | 高级检索  
    按 检索      


Variational Operators,Symplectic Operators,and the Cohomology of Scalar Evolution Equations
Authors:ME Fels  E Ya?ar
Institution:1. Department of Mathematics and Statistics, Utah State University, Logan Utah, 84322, USA;2. Department of Mathematics, Uludag University, Bursa, Turkey eyasar@uludag.edu.tr
Abstract:For a scalar evolution equation ut = K(t, x, u, ux, . . . , u2m+1) with m ≥ 1, the cohomology space H1,2( /></span>) is shown to be isomorphic to the space of variational operators and an explicit isomorphism is given. The space of symplectic operators for <i>u<sub>t</sub></i> = <i>K</i> for which the equation is Hamiltonian is also shown to be isomorphic to the space <i>H</i><sup>1,2</sup>(<span class= /></span>) and subsequently can be naturally identified with the space of variational operators. Third order scalar evolution equations admitting a first order symplectic (or variational) operator are characterized. The variational operator (or symplectic) nature of the potential form of a bi-Hamiltonian evolution equation is also presented in order to generate examples of interest.</td> </tr> <tr> <td align=
Keywords:Variational Bicomplex  Cohomology  Scalar Evolution Equation  Symplectic Operator  Hamiltonian Evolution Equation
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号