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 purpose of this paper is to analyze in detail a special nonlinear partial differentialequation (npde) of the second order which is important in physical, chemical and technicalapplications. the present npde describes nonlinear diffusion and is of interest in several partsof physics, chemistry and engineering problems alike. since nature is not linear intrinsicallythe nonlinear case is there...

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and...

The knowledge of exact symmetries of a diierential problem allows to reduce it, and sometimes to completely solve it; it also allows to obtain exact solutions. If we are looking for approximate rather than exact solutions, then approximate symmetries are as good as exact ones; moreover, they can be determined perturbatively. In this paper we introduce and study approximate symmetries, together ...

Quasisymmetry builds a third invariant for charged-particle motion besides energy and magnetic moment. We address quasisymmetry at the level of approximate symmetries first-order guiding-centre motion. find that conditions to leading order are same as exact if one insists symmetry is purely spatial. also generalise allow phase-space symmetries, derive weaker conditions. The latter recover "weak...