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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)

- Gadi Fibich, Boaz Ilan, Steven Schochet
- 2003

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)

We show that the increase in critical power for elliptic input beams is only 40% of what had been previously estimated based on the aberrationless approximation. We also find a theoretical upper bound for the critical power, above which elliptic beams always collapse. If the power of an elliptic beam is above critical, the beam self-focuses and undergoes… (More)

The explicit contribution to the free energy barrier and proton conductance from the delocalized nature of the excess proton is examined in aquaporin channels using an accurate all-atom molecular dynamics computer simulation model. In particular, the channel permeation free energy profiles are calculated and compared for both a delocalized (fully Grotthuss… (More)

The critical nonlinear Schrödinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L 2 norm of the… (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)

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)

In this study, the minimalist synthetic LS2 channel is used as a prototype to examine the selectivity of protons over other cations. The free-energy profiles along the transport pathway of LS2 are calculated for three cation species: a realistic delocalized proton (including Grotthuss shuttling)--H(+), a classical (nonshuttling) hydronium--H(3)O(+), and a… (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)