共查询到20条相似文献,搜索用时 140 毫秒
1.
Theoretical and Mathematical Physics - We present an infinite series of autonomous discrete equations on a square lattice with hierarchies of autonomous generalized symmetries and conservation laws... 相似文献
2.
Jing Ping Wang 《Studies in Applied Mathematics》2012,129(3):309-327
We construct a recursion operator for the family of Narita–Itoh–Bogoyavlensky infinite lattice equations using its Lax presentation and present their mastersymmetries and bi‐Hamiltonian structures. We show that this highly nonlocal recursion operator generates infinitely many local symmetries. 相似文献
3.
We construct the Darboux transformations, exact solutions, and infinite number of conservation laws for a semidiscrete Gardner equation. A special class of solutions of the semidiscrete equation, called table-top solitons, are given. The dynamical properties of these solutions are also discussed. 相似文献
4.
The vertex-labeling of graphs with nonnegative integers provides a natural setting in which to study problems of radio channel assignment. Vertices correspond to transmitter locations and their labels to radio channels. As a model for the way in which interference is avoided in real radio systems, each pair of vertices has, depending on their separation, a constraint on the difference between the labels that can be assigned. We consider the question of finding labelings of minimum span, given a graph and a set of constraints. The focus is on the infinite triangular lattice, infinite square lattice, and infinite line lattice, and optimal labelings for up to three levels of constraint are obtained. We highlight how accepted practice can lead to suboptimal channel assignments. © 1998 John Wiley & Sons, Inc. J Graph Theory 29: 263–283, 1998 相似文献
5.
We consider a Darboux transformation of a generalized lattice (or semidiscrete) Heisenberg magnet (GLHM) model. We define a Darboux transformation on solutions of the Lax pair and on solutions of the spin evolution equation of the GLHM model. The solutions are expressed in terms of quasideterminants. We give a general expression for K-soliton solutions in terms of quasideterminants. Finally, we obtain one- and two-soliton solutions of the GLHM model using quasideterminant properties. 相似文献
6.
Theoretical and Mathematical Physics - Based on a determining equation set and master function, we consider a Cauchy matrix scheme for three semidiscrete lattice Korteweg–de Vries-type... 相似文献
7.
研究非Chetaev型变质量非完整系统的Lie对称性与Noether对称性以及其间的 关系,给出Lie对称性导致Noether对称性以及Noether对称性导致Lie对称性的条件. 相似文献
8.
Consider a general variational problem of a functional whose domain of definition consists of integral manifolds of an exterior differential system. In particular, this induces classical variational problems with constraints. With the assumption of existence of enough admissable variations the Euler-Lagrange equations associated to this problem are obtained. By studying a spectral sequence associated to the infinite prolongation of them, we extend the classical notion of infinitesimal Noether symmetries to what we shall call the “higher order Noether symmetries,” and a higher order Noether's theorem identifying the higher order conservation laws and the higher order Noether symmetries is obtained. These in turn are isomorphic to the solution space of certain linear differential operator. From these we also get a systematic method of computing the higher order conservation laws of certain determined PDE systems. 相似文献
9.
We prove that random-cluster models with \(q \ge 1\) on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter \(p_c\) below which the model exhibits exponential decay and above which there exists a.s. an infinite cluster. The result may be extended to the Potts model via the Edwards–Sokal coupling. Our method is based on sharp threshold techniques and certain symmetries of the lattice; in particular it makes no use of self-duality. Part of the argument is not restricted to planar models and may be of some interest for the understanding of random-cluster and Potts models in higher dimensions. Due to its nature, this strategy could be useful in studying other planar models satisfying the FKG lattice condition and some additional differential inequalities. 相似文献
10.
This paper describes symmetries of all integrable difference equations that belong to the famous Adler–Bobenko–Suris classification. For each equation, the characteristics of symmetries satisfy a functional equation, which we solve by reducing it to a system of partial differential equations. In this way, all five-point symmetries of integrable equations on the quad-graph are found. These include mastersymmetries, which allow one to construct infinite hierarchies of local symmetries. We also demonstrate a connection between the symmetries of quad-graph equations and those of the corresponding Toda type difference equations. 相似文献
11.
A synaptic algebra is a generalization of the Jordan algebra of self-adjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence relation on the projection lattice of the algebra induced by finite sequences of symmetries. In case the projection lattice is complete, or even centrally orthocomplete, this equivalence relation is shown to possess many of the properties of a dimension equivalence relation on an orthomodular lattice. 相似文献
12.
Anton V. Eremeev & Alexander S. Yurkov 《高等学校计算数学学报(英文版)》2023,16(2):370-392
Solution and analysis of mathematical programming problems may be
simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help decrease the problem dimension, reduce the size of the search space by means of linear cuts. While
the previous studies of symmetries in the mathematical programming usually dealt
with permutations of coordinates of the solutions space, the present paper considers
a larger group of invertible linear transformations. We study a special case of the
quadratic programming problem, where the objective function and constraints are
given by quadratic forms. We formulate conditions, which allow us to transform the
original problem to a new system of coordinates, such that the symmetries may be
sought only among orthogonal transformations. In particular, these conditions are
satisfied if the sum of all matrices of quadratic forms, involved in the constraints,
is a positive definite matrix. We describe the structure and some useful properties
of the group of symmetries of the problem. Besides that, the methods of detection
of such symmetries are outlined for different special cases as well as for the general
case. 相似文献
13.
V. Rosenhaus 《Theoretical and Mathematical Physics》2005,144(1):1046-1053
We consider partial differential equations of variational problems with infinite symmetry groups. We study local conservation laws associated with arbitrary functions of one variable in the group generators. We show that only symmetries with arbitrary functions of dependent variables lead to an infinite number of conservation laws. We also calculate local conservation laws for the potential Zabolotskaya-Khokhlov equation for one of its infinite subgroups.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 190–198, July, 2005. 相似文献
14.
Elliptic reconstruction and a posteriori error estimates for parabolic optimal control problems
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In this article, a semidiscrete finite element method for parabolic optimal control problems is investigate. By using elliptic reconstruction, a posteriori error estimates for finite element discretizations of optimal control problem governed by parabolic equations with integral constraints are derived. 相似文献
15.
A straightforward algorithm for the symbolic computation of generalized (higher‐order) symmetries of nonlinear evolution equations
and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the
polynomial form of the generalized symmetries. The coefficients of the symmetry can be found by solving a linear system. The
method applies to polynomial systems of PDEs of first order in time and arbitrary order in one space variable. Likewise, lattices
must be of first order in time but may involve arbitrary shifts in the discretized space variable.
The algorithm is implemented in Mathematica and can be used to test the integrability of both nonlinear evolution equations
and semi‐discrete lattice equations. With our Integrability Package, generalized symmetries are obtained for several well‐known
systems of evolution and lattice equations. For PDEs and lattices with parameters, the code allows one to determine the conditions
on these parameters so that a sequence of generalized symmetries exists. The existence of a sequence of such symmetries is
a predictor for integrability.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
16.
R. Sahadevan S. Khousalya L. Nalini Devi 《Journal of Mathematical Analysis and Applications》2005,308(2):636-655
A systematic method to derive the nonlocal symmetries for partial differential and differential-difference equations with two independent variables is presented and shown that the Korteweg-de Vries (KdV) and Burger's equations, Volterra and relativistic Toda (RT) lattice equations admit a sequence of nonlocal symmetries. An algorithm, exploiting the obtained nonlocal symmetries, is proposed to derive recursion operators involving nonlocal variables and illustrated it for the KdV and Burger's equations, Volterra and RT lattice equations and shown that the former three equations admit factorisable recursion operators while the RT lattice equation possesses (2×2) matrix factorisable recursion operator. The existence of nonlocal symmetries and the corresponding recursion operator of partial differential and differential-difference equations does not always determine their mathematical structures, for example, bi-Hamiltonian representation. 相似文献
17.
We define an infinite class ?4 of infinite lattices with the property that every finitely generated infinite lattice of width four contains (up to duality) a sublattice isomorphic to the herringbone or to a member of ?4. A consequence is that every finitely generated infinite lattice of width four generates a variety of infinite height (in the lattice of varieties of lattices). 相似文献
18.
Marc Henneaux Axel Kleinschmidt Gustavo Lucena Gómez 《Proceedings of the Steklov Institute of Mathematics》2011,272(1):141-150
Gauge symmetries lead to first-class constraints. This assertion is, of course, true only for non-trivial gauge symmetries,
i.e., gauge symmetries that act non-trivially on-shell on the dynamical variables. We illustrate this well-appreciated fact
for time reparametrization invariance in the context of modifications of gravity-suggested in a recent proposal by Hořava-in
which the Hamiltonian constraint is deformed by arbitrary spatial diffeomorphism invariant terms, where some subtleties are
found to arise. 相似文献
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20.
研究非齐次Toda晶格,即一类非齐次非线性微分差分方程的对称与可积性。给出了这一类方程的Lie点对称,条件对称和精确解。给出这类方程与Toda晶格之间的可逆点变换,从而表明这一类方程是可积的。 相似文献