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We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion iψt ± ∆ q ψ + |ψ| 2σ ψ = 0, in the isotropic mixed-dispersion NLS iψt + ∆ψ + ǫ∆ 2 ψ + |ψ| 2σ ψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays. 1. Introduction. The canonical model for… (More)

The nonlinear Schrödinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the non-linear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way… (More)

We calculate the critical exponent of nonlinear Schrödinger (NLS) equations with anisotropic negative fourth-order dispersion using an anisotropic Gagliardo–Nirenberg inequality. We also prove global existence, and in some cases uniqueness, for subcritical solutions and for critical solutions with small L 2 norm, without making use of Strichartz-type… (More)

- Gadi Fibich, Boaz Ilan
- 2001

The standard explanation for multiple filamentation of laser beams is that breakup of cylindrical symmetry is initiated by noise in the input beam. In this study we propose an alternative deterministic explanation based on vectorial effects. We derive a scalar equation from the vector Helmholtz equation that describes self-focusing in the presence of… (More)

Localized nonlinear modes, or solitons, are obtained for the two-dimensional nonlinear Schrödinger equation with various external potentials that possess large variations from periodicity, i.e., vacancy defects, edge dislocations, and quasicrystal structure. The solitons are obtained by employing a spectral fixed-point computational scheme. Investigation of… (More)

A nonlinear model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the fully nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm.… (More)

We provide what is to our knowledge the first experimental evidence that multiple filamentation (MF) of ultra-short pulses can be induced by input beam ellipticity. Unlike noise-induced MF, which results in complete beam breakup, the MF pattern induced by small input beam ellipticity appears as a result of nucleation of annular rings surrounding the central… (More)

The standard explanation for multiple filamentation of laser pulses is that it is caused by noise in the input beam. We propose an alternative explanation that is based on deterministic vectorial (polarization) effects. We present numerical simulations in support of the vectorial-effects explanation and suggest a simple experiment for deciding whether… (More)

The relation between the fundamental parameters of energy and temporal duration of ultrashort pulses, under the condition of varying the average dispersion, are demonstrated both theoretically and experimentally in a solid-state femtosecond mode-locked laser. An asymptotic theory for nonlinear and dispersion managed solitons agrees well with the… (More)