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Lie Symmetries of Differential Equations: Classical Results and Recent Contributions
  • F. Oliveri
  • Mathematics, Computer Science
    Symmetry
  • 8 April 2010
TLDR
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.
Dynamics and wave propagation in dilatant granular materials
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
When nonautonomous equations are equivalent to autonomopus ones
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
Nonlinear wave propagation in a non-diffusive model of bubbly liquids
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
Reduction to autonomous form by group analysis and exact solutions of axisymmetric MHD equations
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
An Operator-Like Description of Love Affairs
TLDR
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.
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