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Ergodic isospectral theory of the Lax pairs of Euler equations with harmonic analysis flavor 总被引:2,自引:0,他引:2
Y. Charles Li 《Proceedings of the American Mathematical Society》2005,133(9):2681-2687
Isospectral theory of the Lax pairs of both 3D and 2D Euler equations of inviscid fluids is developed. Eigenfunctions are represented through an ergodic integral. The Koopman group and mean ergodic theorem are utilized. Further harmonic analysis results on the ergodic integral are introduced. The ergodic integral is a limit of the oscillatory integral of the first kind.
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We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose
corresponding Bieberbach groups have the canonical lattice as translation lattice. By using the explicit expression of the
heat trace of the Laplacian acting on p-forms, we determine all p-isospectral and L-isospectral pairs and we show that in this class of manifolds, isospectrality on functions and isospectrality on p-forms for all values of p are equivalent to each other. The list shows for any p, 1 ≤ p ≤ 3, many p-isospectral pairs that are not isospectral on functions and have different lengths of closed geodesics. We also determine
all length isospectral pairs (i.e. with the same length multiplicities), showing that there are two weak length isospectral
pairs that are not length isospectral, and many pairs, p-isospectral for all p and not length isospectral.
Mathematics Subject Classifications (2000): 58J53, 58C22, 20H15. 相似文献
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We construct a series of pairs of domains in the plane and pairs of surfaces with boundary that are isospectral but not isometric.
The construction is based on the existence of finite transformation groups that are spectrally equivalent but not isomorphic.
Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 660–664, May, 1998.
This research was partially supported by the Russian Foundation for Basic Research and by INTAS under joint grant No. 96-01-00043. 相似文献
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基于一个带有三个位势函数新的等谱问题,本文得到了一个带有任意函数的新的Lax可积族.当位势选取特殊函数时,得到了著名的Schrodinger方程,广义MkdV方程,热传导方程和耦合的Burgers方程及其Hamiltonian结构,并证明方程是Liouville可积的. 相似文献
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赵晶 《数学的实践与认识》2007,37(8):61-65
构造了一类3×3的反对称loop代数,由此设计了一个含5个位势函数的等谱问题;利用屠格式导出了一个Liouville可积系统,且拥有双Hamilton结构. 相似文献
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Russell Merris 《Linear and Multilinear Algebra》1997,43(1):201-205
Two graphs are isomorphic only if they are Laplacian isospectral, that is, their Laplacian matrices share the same multiset of eigenvalues. Large families of nonisomorphic Laplacian isospectral graphs are exhibited for which the common multiset of eigenvalues consists entirely of integers. 相似文献
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** Email: h.gottlieb{at}griffith.edu.au By utilizing transformations of both the radial coordinate andthe radial wave function, densities of annular membranes whichare radially isospectral to any given radial density are produced.In particular, new families of annular membrane densities arefound which are radially isospectral to a uniform membrane.Some new generalizations for completely isospectral annularmembranes (including angle-dependent densities) are also given. 相似文献
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借助双Casoratian技巧和构造双Wronski行列式元素的矩阵方法,求出2个位势的Ablowitz-Ladik等谱方程的Complexiton解和周期解,并通过将矩阵取成不同的组合类型,进而分别得到该方程具有双Casorati行列式形式的新解,即Complexiton解与类有理解的混合解、Complexiton解与Matveev解的混合解. 相似文献