On the cubic and cubic-quintic optical vortices equations
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Carlo Greco
Abstract
An optical vortex can appear when a light beam with nonzero angular momentum propagates in a suitable nonlinear medium. In some situations has been observed that the light intensity vanish at the center of the vortex (where the phase of the electromagnetic field is undefined), while the light beam assumes a ring-shaped structure. In this paper we consider two classical cases in which such kind of phenomena occur: the case of the self focusing cubic nonlinearity, and the case of competing quintic and cubic nonlinearity. In both cases we study the nonlinear Schrödinger equation of the optical field (with various boundary conditions) by means of min-max methods, and we prove the existence of saddle point type solutions, as well as minimum type solutions.
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- On the cubic and cubic-quintic optical vortices equations
- Symmetry reductions and exact solutions to the Sharma–Tasso–Olever equation
- Simultaneously proximinal subspaces
- Iteration regularized semigroups of set-valued functions
- A recursive-operational approach with applications to linear differential systems
- On symmetrically porouscontinuous functions
- Compactness result and its applications in integral equations
-
On statistically
- Ritz-least squares method for finding a control parameter in a one-dimensional parabolic inverse problem
Articles in the same Issue
- Frontmatter
- On the cubic and cubic-quintic optical vortices equations
- Symmetry reductions and exact solutions to the Sharma–Tasso–Olever equation
- Simultaneously proximinal subspaces
- Iteration regularized semigroups of set-valued functions
- A recursive-operational approach with applications to linear differential systems
- On symmetrically porouscontinuous functions
- Compactness result and its applications in integral equations
-
On statistically
- Ritz-least squares method for finding a control parameter in a one-dimensional parabolic inverse problem
