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pro vyhledávání: '"35"'
Autor:
Li, Y. Charles
Publikováno v:
Dynamics of PDE, Vol.3, no.3, (2006), 235-258
In this article, we prove the existence of Arnold diffusion for an interesting specific system -- discrete nonlinear Schr\"odinger equation. The proof is for the 5-dimensional case with or without resonance. In higher dimensions, the problem is open.
Externí odkaz:
http://arxiv.org/abs/math/0607443
Autor:
Li, Yanguang Charles
In this paper, we study the discrete cubic nonlinear Schroedinger lattice under Hamiltonian perturbations. First we develop a complete isospectral theory relevant to the hyperbolic structures of the lattice without perturbations. In particular, Backl
Externí odkaz:
http://arxiv.org/abs/math/0302197
Autor:
Li, Yanguang Charles
The global regularity for the viscous Boussinesq equations is proved.
Comment: Mathematical Methods in Appl. Sci. (in press)
Comment: Mathematical Methods in Appl. Sci. (in press)
Externí odkaz:
http://arxiv.org/abs/math/0302199
Autor:
Li, Yanguang Charles
For a general evolution equation with a Silnikov homoclinic orbit, Smale horseshoes are constructed.
Comment: Mathematical and Computer Modelling (in press)
Comment: Mathematical and Computer Modelling (in press)
Externí odkaz:
http://arxiv.org/abs/math/0302198
Autor:
Li, Yanguang Charles
Recently, the author and collaborators have developed a systematic program for proving the existence of homoclinic orbits in partial differential equations. Two typical forms of homoclinic orbits thus obtained are: (1). transversal homoclinic orbits,
Externí odkaz:
http://arxiv.org/abs/math/0302200
Autor:
Li, Yanguang Charles
The spectral theorem of the linear 2D Euler operator in Sobolev spaces is presented as a corollary of the spectral theorem in $\ell_2$ space in [Li,00]. Study on the (dashed) line model introduced in [Li,01] is continued. Specifically, invariant mani
Externí odkaz:
http://arxiv.org/abs/math/0206278
Autor:
Li, Yanguang Charles
Publikováno v:
Studies in Applled Mathematics, 2002, current issue
Singularly perturbed vector nonlinear Schroedinger equations (PVNLS) are investigated. Emphasis is placed upon the relation with their restriction: The singularly perturbed scalar nonlinear Schroedinger equation (PNLS) studied earlier by Li. It turns
Externí odkaz:
http://arxiv.org/abs/math/0205113
Autor:
LI, Yanguang Charles
Publikováno v:
Proceedings of Institute of Mathematics of NAS of Ukraine: Proceedings of the Fourth International Conference SYMMETRY in Nonlinear Mathematical Physics, 2002
In this article, I will report a Lax pair structure, a Backlund-Darboux transformation, and the investigation of homoclinic structures for 2D Euler equations of incompressible inviscid fluids.
Externí odkaz:
http://arxiv.org/abs/math/0205115
Autor:
Li, Yanguang Charles
In Part I of our study on 2D Euler equation, we established the spectral theorem for a linearized 2D Euler equation. We also computed the point spectrum through continued fractions, and identified the eigenvalues with nonzero real parts. In this Part
Externí odkaz:
http://arxiv.org/abs/math/0010200
Autor:
Arathoon, Philip
We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class which we call normal, and a non-generic abnormal class. The eigenvalues of
Externí odkaz:
http://arxiv.org/abs/2310.15035