Related papers: Symmetry in variational principles and application…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in [Hydon, {\it Proc. R. Soc. A}, 461, 1627--1637, 2005]. The…
This note presents an attempt to provide a conceptual framework for variational formulations of classical physics. Variational principles of physics have all a common source in the {\it principle of virtual work} well known in statics of…
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…
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an…
This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual…
We apply Lie symmetry analysis of partial differential equations (PDEs) to the Euler-Lagrange equations of the two-Higgs-doublet model (2HDM), to determine its scalar Lie point symmetries. A Lie point symmetry is a structure-preserving…
The critical variational setting was recently introduced and shown to be applicable to many important SPDEs not covered by the classical variational setting. In this paper, we extend the critical variational setting in several ways. We…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
Symmetry distills the simplicity of natural laws from the complexity of physical phenomena. The symmetry principle is of vital importance in various aspects of modern physics, including analyzing atomic spectra, determining fundamental…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
We introduce a technique to solve numerically the relativistic Euler's equations in scenarios with spherical symmetry using the standard Smoothed Particles Hydrodynamics method in cartesian coordinates. This implementation allow us to…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical…
We investigate the relation between pluri-Lagrangian hierarchies of $2$-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings…
For variational problems with $O(N)$-symmetry the existence of several geometrically distinct solutions had been shown by use of group theoretic approach in previous articles. It was done by a crafty choice of a family $H_i \subset O(N)$…