We consider the 3D equation $u_{yy} = u_{tx} + u_yu_{xx} - u_xu_{xy}$ and its 2D reductions: (1) (u_y+y)u_{xx}-u_xu_{xy}-2$ (which is equivalent to Gibbons-Tsarev equation) (2) (u_y+2x)u_{xx} (y-u_x)u_{xy} -u_x$. Using reduction of known Lax pair for equation, we describe nonlocal symmetries of~(1) and~(2) show that Lie algebras these are isomorphic Witt algebra.

Abstract A Lie system is a non-autonomous of first-order ordinary differential equations describing the integral curves vector field taking values in finite-dimensional real algebra fields, so-called Vessiot–Guldberg algebra. In this work, multisymplectic forms are applied to study reduction systems through their symmetries. By using momentum map, we perform and reconstruction procedure systems...

let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

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In the present work, we consider non-minimal coupling inflationary model in context of constant-roll idea which is investigated by first-order formalism. We attempt to find hidden symmetries behind Lie symmetry method. supply this aim using features Heun function instead Killing vector approach. show that inflation cases power-law and exponential couplings are characterized as a generalized for...

‎In this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎We show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a Lie groupoid‎. ‎Using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the Lie algebra of all vector fields on the smooth...

In this paper, we study possible mathematical connections of the Clifford algebra with su(N)-Lie algebra, or in more physical terms links between space-time symmetry (Lorentz invariance) and internal SU(N) gauge-symmetry for a massive spin one-half fermion described by Dirac equation. The related matrix is worked out particular SU(2) outlined as well color gauge group SU(3). Possible perspectiv...