Geometric Discretisation of the Toda System
نویسنده
چکیده
The Laplace sequence of the discrete conjugate nets is constructed. The invariants of the nets satisfy, in full analogy to the continuous case, the system of difference equations equivalent to the discrete version of the generalized Toda equation.
منابع مشابه
The Algebro-geometric Toda Hierarchy Initial Value Problem for Complex-valued Initial Data
We discuss the algebro-geometric initial value problem for the Toda hierarchy with complex-valued initial data and prove unique solvability globally in time for a set of initial (Dirichlet divisor) data of full measure. To this effect we develop a new algorithm for constructing stationary complex-valued algebro-geometric solutions of the Toda hierarchy, which is of independent interest as it so...
متن کاملThe Finite Non-periodic Toda Lattice: a Geometric and Topological Viewpoint
In 1967, Japanese physicist Morikazu Toda published the seminal papers [78] and [79], exhibiting soliton solutions to a chain of particles with nonlinear interactions between nearest neighbors. In the decades that followed, Toda’s system of particles has been generalized in different directions, each with its own analytic, geometric, and topological characteristics that sets it apart from the o...
متن کاملGeometric Logical Operations for Type-2 Fuzzy Sets
This paper presents a series of geometric definitions and algorithms that together form a type-2 geometric fuzzy inference system which can operate over a truly continuous domain, with no need for discretisation at any stage.
متن کاملGeometric Engineering of N=1 Quantum Field Theories
We construct local geometric model in terms of Fand M-theory compactification on Calabi-Yau fourfolds which lead to N = 1 Yang-Mills theory in d = 4 and its reduction on a circle to d = 3. We compute the superpotential in d = 3, as a function of radius, which is generated by the Euclidean 5-brane instantons. The superpotential turns out to be the same as the potential for affine Toda theories. ...
متن کاملA Cubic Whitney and Further Developments in Geometric Discretisation
Geometric discretisation draws analogies between discrete objects and operations on a complex with continuum ones on a manifold. We generalise the theory to the cubic case and incorporate metric, by adding volume factors to our discrete Hodge star and then by modifying our inner product which leads to the same result.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997