For the inflaton field we determine a new exact solution by using Lie symmetry analysis. Specifically, construct second-order differential master equation for arbitrary scalar potential assuming that spectral index density perturbations $n_{s}$ and to tensor ratio $r$ are related as $n_{s}-1=h\left( r\right) $. Function $h\left( $ is classified according admitted symmetries equation. The possib...

It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an n − 1 area enclosing a constant n-volume in a Euclidean space is so n ⊕sR and in a space of constant curvature the Lie algebra is so n . Furthermore, if the space has one section of constant curvature of dimension n1, another of n2, and so on to nk and one of zero curvature of dimension m, with n ≥ ∑kj 1 nj ...

Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial first-order approximate symmetry.

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational “dynamical exponent”, z. The Schrödinger-Virasoro algebra of Henkel et ...

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational “dynamical exponent”, z. The Schrödinger-Virasoro algebra of Henkel et ...

A constructive algorithm is proposed for the investigation of symmetries of partial differential equations. The algorithm is used to present classical Lie symmetries of systems of two non-linear reaction diffusion equations.

The paper presents a connection between Lie symmetries and conservation laws for the 2D Ricci flow model.The procedure starts by obtaining a set of multipliers which generates conservation laws.Then, taking into account the most general form of multiplier and making use of a relation which connects Lie symmetries and conservation laws for any dynamical system, one determines associated symmetry...

arising in several application [4]. Lie symmetry of BEq was found in [5], while the Q-conditional symmetry (i.e., non-classical symmetry [6]) was described in [7] and [8]. In the general case a wide list of Lie symmetries for DC equations of the form (1) is presented in [9]. A complete description of Lie symmetries, i.e., group classification of (1) has been done in [10]. The Q-conditional symm...

Different deformations of the Poincaré symmetries have been identified for various non-commutative spaces (e.g. κ-Minkowski, sl(2, R), Moyal). We present here the deformation of the Poincaré symmetries related to Snyder space-time. The notions of smooth “K-loop”, a non-associative generalization of Abelian Lie groups, and its infinitesimal counterpart given by the Lie triple system are the key ...