"Optimal systems" of similarity solutions of a given system of nonlinear partial (integro-)differential equations which admits a finite-dimensional Lie point symmetry group G are an effective systematic means to classify these group-invariant solutions since every other such solution can be derived from the members of the optimal systems. The classification problem for the similarity solutions ...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

We extend our analysis on the Lie symmetries in fluid dynamics to case of macroscopic traffic estimation models. In particular we study Aw–Rascle–Zhang model for estimation, which consists two hyperbolic first-order partial differential equations. The symmetries, one-dimensional optimal system and corresponding invariants are determined. Specifically, find that admitted form four-dimensional al...

A construction of W-symmetries is given only in terms of the nonlocal fields (parafermions ψ α), which take values on the homogeneous space G/U (1) r , where G is a simply connected compact Lie group manifold (its accompanying Lie algebra G is a simple one of rank r). Only certain restriction of the root set of Lie algebra on which the parafermionic fields take values are satisfied, then a cons...

For a manifold $M$ with an integral closed 3-form $\omega$, we construct $PU(H)$-bundle and Lie groupoid over its total space, together curving in the sense of gerbes. If form is non-degenerate, furthermore give natural 2-algebra quasi-isomorphism from observables $(M,\omega)$ to weak symmetries above geometric structure, generalising prequantisation map Kostant Souriau.

We investigate the symmetry properties of hierarchies of non-linear Schrödinger equations, introduced in [1], which describe non-interacting systems in which tensor product wave-functions evolve by independent evolution of the factors (the separation property). We show that there are obstructions to lifting symmetries existing at a certain number of particles to higher numbers. Such obstruction...

Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related with the classical shallow water model with the change of variables. The derived symmetries are used to generate new exact solutions of the rotating shallow eq...

Abstract In this paper, approximate Noether and Lie symmetries of 2nd order for Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) charged black hole in the Einstein frame are analyzed comprehensively. To explore order, Minkowski spacetime used which forms a 17 dimensional algebra. It is observed that no new symmetry obtained at 1st order. examine GMGHS spacetime, 35 (exact) an algebra sl (6, ...

Conditional and Lie symmetries of semi-linear 1D Schrödinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrödinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf3)C. We consider non-hermitian re...

In this paper, we formulate an automatic approach to the detection of partial, local, and global symmetries and orbits in arbitrary 3D datasets. We improve upon existing voting-based symmetry detection techniques by leveraging the Lie group structure of geometric transformations. In particular, we introduce a logarithmic mapping that ensures that orbits are mapped to linear subspaces, hence uni...