相关论文: Group Invariant Solutions in Mathematical Physics …

A family of vector fields that are the infinitesimal generators of determined one-parameter groups of transformations are constructed. It is shown that these vector fields represent symmetries of the system of differential equations…

In this lectures I explain a connection between geometric invariant theory and entanglement, and give a number of examples how this approach works.

We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…

Using the basic prolongation method and the infinitesimal criterion of invariance, we find the most general Lie point symmetries group of the Thomas equation. Looking the adjoint representation of the obtained symmetry group on its Lie…

We study actions of linear algebraic groups on central simple algebras using algebro-geometric techniques. Suppose an algebraic group G acts on a central simple algebra A of degree n. We are interested in questions of the following type:…

It is known that action is invariant in special relativity. The goal of this note is to show that the reverse statement is also correct, that special relativity follows from the postulate that action is invariant under the transformation…

The present article studies the potential form of the nonlinear Gardner-Kawahara equation through the perspective of Lie symmetry analysis. Lie symmetry analysis was used to investigate abundant group-invariant solutions of the nonlinear…

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…

A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to…

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

A systematic group-theoretical analysis of the supersymmetric sinh-Gordon equation is performed. A generalization of the method of prolongations is used to determine the Lie superalgebra of symmetries, and the method of symmetry reduction…

Given an action of a reductive group on a normal variety, we construct all invariant open subsets admitting a good quotient with a quasiprojective or a divisorial quotient space. Our approach extends known constructions like Mumford's…

Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…

In this paper, we show that when two systems of differential equations admitting a symmetry group are related by a point transformation it is always possible to generate invariant schemes, one for each system, that are also related by the…

Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…

The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…

For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…