Some finite dimensional integrable systems
نویسندگان
چکیده
منابع مشابه
Bäcklund Transformations for Finite-dimensional Integrable Systems: a Geometric Approach
We present a geometric construction of Bäcklund transformations and discretizations for a large class of algebraic completely integrable systems. To be more precise, we construct families of Bäcklund transformations, which are naturally parametrized by the points on the spectral curve(s) of the system. The key idea is that a point on the curve determines, through the Abel-Jacobi map, a vector o...
متن کاملFinite-dimensional integrable systems associated with Davey-Stewartson I equation
For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems with a constraint of Neumann type. The full set of involutive conserved integrals is obtained ...
متن کاملSolution of some integrable one-dimensional quantum systems.
In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential. We show these systems to be integrable, and exploit this integrability to completely determine the spectrum including degeneracy, and thus the thermodynamics...
متن کاملSome Integrable Quantum Systems on the Lattice
The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is attracting more interest due to the lattice field theories and the hypothesis of a finite space. 1 Weyl group on finite space We defined the position space of dimens...
متن کاملOrbital Maghetism in Two-Dimensional Integrable Systems
We study orbital magnetism of a degenerate electron gas in a number of twodimensional integrable systems, within linear response theory. There are three relevant
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1978
ISSN: 0035-7596
DOI: 10.1216/rmj-1978-8-1-237