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Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification is such that...

Heteroclinic orbits in plane dynamical systems

Luisa Malaguti, Cristina Marcelli (2002)

Archivum Mathematicum

We consider general second order boundary value problems on the whole line of the type u ' ' = h ( t , u , u ' ) , u ( - ) = 0 , u ( + ) = 1 , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the ( u , u ' ) plane dynamical system.

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