arXiv subjects

J. Nasarre

Publications and source records attributed to J. Nasarre.

4 recordsLinked to original sources

arXiv1998

The nonlinear superposition principle and the Wei-Norman method

Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei-Norman method is applied to obtain the associated differential equation in the group $SL(2,R)$. The superposition principle for first order differential equation systems and Lie-Scheffers theorem are also analysed from this group theoretical perspective. Finally, the theory is applied in the solution of second order differential equations like time-independent Schroedinger equation

math-ph↗

arXiv1997

Symplectic and Lie algebraic techniques in Geometric Optics

We will show the usefulness of the tools of Symplectic and Presymplectic Geometry and the corresponding Lie algebraic methods in different problems in Geometric Optics.

physics.optics↗

arXiv1996

On the symplectic structures arising in Optics

Geometric optics is analysed using the techniques of Presymplectic Geometry. We obtain the symplectic structure of the space of light rays in a medium of a non constant refractive index by reduction from a presymplectic structure, and using adapted coordinates, we find Darboux coordinates. The theory is illustrated with some examples and we point out some simple physical applications

hep-th↗

arXiv1996

Presymplectic Geometry and Fermat's Principle for anisotropic media

The tools of presymplectic geometry are used to study light rays trajectories in anisotropic media.

hep-th↗