arXiv subjects

Hector E. Nistazakis

Publications and source records attributed to Hector E. Nistazakis.

2 recordsLinked to original sources

arXiv2009

Dynamical oscillations in nonlinear optical media

The spatial dynamics of pulses in Kerr media with parabolic index profile are examined. It is found that when diffraction and graded-index have opposite signs propagating pulses exhibit an oscillatory pattern, similar to a breathing behavior. Furthermore, if the pulse and the index profile are not aligned the pulse oscillates around the index origin with frequency that depends on the values of the diffraction and index of refraction. These oscillations are not observed when diffraction and graded-index share the same sign.

physics.optics↗

arXiv2005

Asymptotic Behavior of Solutions of Complex Discrete Evolution Equations: The Discrete Ginzburg-Landau Equation

We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dynamical behavior ranging from global existence of solutions and global attractors, to blow up in finite time. We provide estimates for the blow up time, depending not only on the initial data but also on the size of the lattice. Some of the theoretical results, are tested by numerical simulations.

math.CA↗