We show that a Minkowski phase space endowed with bracket relatively to conformable differential realizes Poisson algebra, confering bi-Hamiltonian structure the resulting manifold. infer related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute corresponding deformed recursion operator. Besides, using Hamiltonian–Jacobi separability, we construct operators for fields i...

In this paper we restrict ourselves to Lie point symmetries an applications to the fourth order generalized Burgers equation GBE4. Using computer programs under the computer algebra package MATHEMATIC A we find a three dimensional solvable Lie algebra of point symmetries of the GBE4 equation. The similarity reductions due to these symmetries have also been obtained. The idea of applying Lie gro...

By applying the Lie symmetry method, group-invariant solutions are constructed for axially loaded Euler beams. The corresponding mathematical models of beams formulated. After introducing infinitesimal transformations, determining equations proposed via point transformations acting on original equations. generators symmetries systems presented with Maple. vector fields given to span subalgebra ...

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...

The coagulation of aerosol particles plays an important role in the structural morphological changes suspended at any time and space. In this study, based on Smoluchowski equation population balance, a kinetic model coalescence considering Brownian motion collision is established. By applying developed Lie group method, we derive allowed infinitesimal symmetries group-invariant solutions integr...

The Lie algebra of infinitesimal CR automorphisms is a fundamental local invariant manifold. Motivated by the Poincaré equivalence problem, we analyze its positively graded components, containing nonlinearizable holomorphic vector fields. results provide complete description weighted homogeneous polynomial models in $$\mathbb C^N$$ , which admit symmetries degree higher than two. For models, wi...

Given a smooth family of unparameterized curves such that through every point in direction there passes exactly one curve, does exist Lagrangian with extremals being precisely this family? It is known dimension 2 the answer positive. In 3, it follows from work Douglas is, general, negative. We generalise result to all higher dimensions and show actually negative for almost curves, also as path ...

The associativity equations, also known as the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations [1, 2], and the related geometric structures, namely, the Frobenius manifolds [3, 4, 5, 6, 7, 8], have recently attracted considerable attention because of their manifold applications in physics and mathematics. More recently, the oriented associativity equations, a generalization of the WDVV equa...

We construct an associative algebra with a decomposition into the direct sum of the underlying vector spaces of another associative algebra and its dual space such that both of them are subalgebras and the natural symmetric bilinear form is invariant or the natural antisymmetric bilinear form is a Connes 2-cocycle. The former is called a double construction of Frobenius algebra and the latter i...