This paper reviews some well known results of Lie group analysis, as well as some recent contributions concerned with the transformation of differential equations to equivalent forms useful to investigate applied problems.Expand

The equations of motion for dilatant granular material are obtained from a Hamiltonian variational principle of local type in the conservative case. The propagation of nonlinear waves in a region… Expand

We consider nonlinear systems of first order partial differential equations admitting at least two one-parameter Lie groups of transformations with commuting infinitesimal operators. Under suitable… Expand

SummaryIn this paper an “ad hoc” asymptotic approach is employed in order to study nonlinear wave propagation compatible with the non-diffusive version of the model of bubbly liquids introduced by… Expand

Motivated by many physical applications, we consider a general first order system of nonlinear partial differential equations involving two independent variables x, t and a vector field u(x,t). We… Expand

The so-called occupation number representation is adopted, originally used in quantum mechanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relations, and analytical conditions for the linear model of the love triangle to have periodic or quasi-periodic solutions are found.Expand