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81.
PENG Yan-Ze E.V. Krishnan 《理论物理通讯》2005,44(11)
The singular manifold method is used to obtain two general solutions to a (2 1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures. 相似文献
82.
Qikeng Lu 《中国科学A辑(英文版)》1998,41(12):1248-1254
In the complex Grassmann manifold ℱ(m,n), the space of complexn-planes passes through the origin of Cm+n; the local coordinate of the space can be arranged into anm ×n matrixZ. It is proved that
is a U(m)-connection of ℱ(m,n) and its curvature form
satisfies the Yang-Mills equation. Moreover,
is an (Sum)-connection and its curvature form
satisfies the Yang-Mills equation.
Project partially supported by the National Natural Science Foundation of China (Grant No. 19631010) and Fundamental Research
Bureau of CAS. 相似文献
83.
84.
Richard C. Penney 《Journal of Functional Analysis》2006,237(1):224-276
Let L be an elliptic operator on a Riemannian manifold M. A function F annihilated by L is said to be L-harmonic. F is said to have moderate growth if and only if F grows at most exponentially in the Riemannian distance. If M is a rank-one symmetric space and L is the Laplace-Beltrami operator for M, the Oshima-Sekiguchi theorem [T. Oshima, J. Sekiguchi, Eigenspaces of invariant differential operators on an affine symmetric space, Invent. Math. 57 (1980) 1-81] states that a L-harmonic function F has moderate growth if and only if F is the Poisson integral of a distribution on the Furstenberg boundary. In this work we prove that this result generalizes to a very large class of homogeneous Riemannian manifolds of negative curvature. We also (i) prove a Liouville type theorem that characterizes the “polynomial-like” harmonic functions which vanish on the boundary in terms of their growth properties, (ii) describe all “polynomial-like” harmonic functions, and (iii) give asymptotic expansions for the Poisson kernel. One consequence of this work is that every Schwartz distribution on the boundary is the boundary value for a L-harmonic function F which is uniquely determined modulo “polynomial-like” harmonic functions. 相似文献
85.
We study the nontrivial Killing vector fields of constant length and the corresponding flows on complete smooth Riemannian manifolds. Various examples are constructed of the Killing vector fields of constant length generated by the isometric effective almost free but not free actions of S 1 on the Riemannian manifolds close in some sense to symmetric spaces. The latter manifolds include “almost round” odd-dimensional spheres and unit vector bundles over Riemannian manifolds. We obtain some curvature constraints on the Riemannian manifolds admitting nontrivial Killing fields of constant length. 相似文献
86.
In this article, Lagrange interpolation by polynomials in several variables is studied. Particularly on the sufficiently intersected algebraic manifolds, we discuss the dimension about the interpolation space of polynomials. After defining properly posed set of nodes (or PPSN for short) along the sufficiently intersected algebraic manifolds, we prove the existence of PPSN and give the number of points in PPSN of any degree. Moreover, in order to compute the number of points in PPSN concretely, we propose the operator ? k with reciprocal difference. 相似文献
87.
In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds. 相似文献
88.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2294-2308
This paper presents an explicit, computationally efficient, recursive formula for computing the normal forms, center manifolds and nonlinear transformations for general n-dimensional systems, associated with semisimple singularities. Based on the formula, we develop a Maple program, which is very convenient for an end-user who only needs to prepare an input file and then execute the program to “automatically” generate the result. Several examples are presented to demonstrate the computational efficiency of the algorithm. 相似文献
89.
In this paper, bifurcation of limit cycles for the degenerate equilibrium to a three- dimensional system is investigated. Firstly, we use formal series to calculate the focal values at the high-order critical point on center manifold. Then an example is studied, and the existence of 3 limit cycles on the center manifold is proved. In terms of high- order singularities in high-dimensional systems, our results are new. 相似文献
90.
The Liouville property of a complete Riemannian manifold M (i.e., the question whether there exist non-trivial bounded harmonic functions on M) attracted a lot of attention. For Cartan–Hadamard manifolds the role of lower curvature bounds is still an open problem.
We discuss examples of Cartan–Hadamard manifolds of unbounded curvature where the limiting angle of Brownian motion degenerates
to a single point on the sphere at infinity, but where nevertheless the space of bounded harmonic functions is as rich as
in the non-degenerate case. To see the full boundary the point at infinity has to be blown up in a non-trivial way. Such examples
indicate that the situation concerning the famous conjecture of Greene and Wu about existence of non-trivial bounded harmonic
functions on Cartan–Hadamard manifolds is much more complicated than one might have expected.
相似文献