The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...

We study the underlying gauge symmetry algebra of the N = 2 string, which is broken down to a subalgebra in any spacetime background. For given toroidal backgrounds, the unbroken gauge symmetries (corresponding to holomorphic and antiholomorphic worldsheet currents) generate area-preserving diffeomorphism algebras of null 2-tori. A minimal Lie algebraic closure containing all the gauge symmetri...

We address the problem of characterisation null-forms conic 3-dimensional systems, that is, control-affine systems whose field admissible velocities forms a (without parameters) in tangent space. Those have been previously identified as simplest control under nonholonomic constraint or zero curvature. In this work, we propose direct among all by studying Lie algebra infinitesimal symmetries. Na...

A complete classification of generalized symmetries of the Yang-Mills equations on Minkowski space with a semi-simple structure group is carried out. It is shown that any generalized symmetry, up to a generalized gauge symmetry, agrees with a first order symmetry on solutions of the Yang-Mills equations. Let g = g1+ · · ·+gn be the decomposition of the Lie algebra g of the structure group into ...

Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms to be projectable to phasespace, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of General Relativity, or other g...

We derive a new four-dimensional partial differential equation with the isospectral Lax representation by shrinking symmetry algebra of reduced quasi-classical self-dual Yang–Mills and applying technique twisted extensions to obtained Lie algebra. Then we find recursion operator for symmetries construct Bäcklund transformation between this Martínez Alonso–Shabat equation. Finally, integrable hi...

In categorified symplectic geometry, one studies the categorified algebraic and geometric structures that naturally arise on manifolds equipped with a closed nondegenerate (n + 1)-form. The case relevant to classical string theory is when n = 2 and is called ‘2-plectic geometry’. Just as the Poisson bracket makes the smooth functions on a symplectic manifold into a Lie algebra, there is a Lie 2...

We consider the 4D Martínez Alonso–Shabat equation E uty=uzuxy−uyuxz (also referred to as universal hierarchy equation) and using its known Lax pair construct two infinite-dimensional differential coverings over E. In these coverings, we give a complete description of Lie algebras nonlocal symmetries. particular, our results generalize ones obtained in Morozov Sergyeyev (2014) contain construct...

We obtain the optimal system’s generating operators associated to a modification of generalization Emden–Fowler Equation. Using those we characterize all invariant solutions generalized. Moreover, present variational symmetries and corresponding conservation laws, using Noether’s theorem Ibragimov’s method. Finally, classify Lie algebra given equation.

All generators of the optimal algebra associated with a generalization Endem-Fowler equation are showed; some them allow to give invariant solutions. Variational symmetries and respective conservation laws also showed. Finally, representation Lie symmetry is showed by groups matrices.