相关论文: On Reduction and Q-conditional (Nonclassical) Symm…

We present classification of Q-conditional symmetries for the two-dimensional nonlinear wave equations and the reductions corresponding to these nonlinear symmetries. Classification of inequivalent reductions is discussed.

New definitions of $Q$-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of $Q$-conditional symmetry of a system generate…

We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of…

Various versions of the definition of nonclassical symmetries existing in the literature are analyzed. Comparing properties of Lie and nonclassical symmetries leads to the conclusion that in fact a nonclassical symmetry is not a symmetry in…

Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true''…

A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…

We review the relation between scale and conformal symmetries in various models and dimensions. We present a dimensional reduction from relativistic to non-relativistic conformal dynamics.

We present full classification of Q-conditional symmetries for the two-dimensional nonlinear wave equation.

A systematic analysis is made of the relations between the symmetries of a classical field and the symmetries of the one-particle quantum system that results from quantizing that field in regimes where interactions are weak. The results are…

An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.

We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…

Contact reduction is very closely related to symplectic reduction, but it allows symmetries that are not manifest in Hamiltonian mechanics and moreover, solution of the reduced problems yields solution of the original problem without…

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…

The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the…

Quantum discord (QD) reveals the nonclassical nature of correlations in bipartite quantum states, going beyond the entanglement-separability paradigm. In this article we discuss the suitability of QD in what concern its possible asymmetry…

It is shown how nonlinear versions of quantum mechanics can be refolmulated in terms of a (linear) C*-algebraic theory. Then also their symmetries are described as automorphisms of the correspondong C*-algebra. The requirement of…

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…

The Lagrangian of Quantum Chromodynamics is invariant under conformal transformations. Although this symmetry is broken by quantum corrections, it has important consequences for strong interactions at short distances and provides one with…

This paper finds a symmetry relation (between quantiles of a random variable and its negative) that is intuitively appealing. We show this symmetry is quite useful in finding new relations for quantiles, in particular an equivariance…

The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…