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- Boaz Ilan, Gadi Fibich, George Papanicolaou
- SIAM Journal of Applied Mathematics
- 2002

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

- Gadi Fibich, Boaz Ilan, Semyon Tsynkov
- J. Sci. Comput.
- 2002

1 School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel. E-mail: {fibich;bazooka}@math.tau.ac.il 2 Department of Mathematics, North Carolina State University, Box 8205, Raleigh, North Carolina 27695. E-mail: tsynkov@math.ncsu.edu. Also: School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978,… (More)

Qudsia Quraishi,* Steven T. Cundiff, Boaz Ilan, and Mark J. Ablowitz Department of Physics, University of Colorado, National Institute of Standards and Technology, and JILA, Boulder, Colorado 80309-0440, USA JILA, National Institute of Standards and Technology, and the University of Colorado, Boulder, Colorado 80309-0440, USA Department of Applied… (More)

- D. E. Mitsotakis, Boaz Ilan, Denys Dutykh
- J. Sci. Comput.
- 2014

A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. The fully-discrete scheme utilizes the Galerkin / finiteelement method based on smooth periodic splines in space, and an explicit fourth-order Runge-Kutta method… (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 L2 norm, without making use of Strichartz-type… (More)

- Y Sivan, G Fibich, B Ilan, M I Weinstein
- Physical review. E, Statistical, nonlinear, and…
- 2008

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multidimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of… (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)

- Gadi Fibich, Shmuel Eisenmann, Boaz Ilan, Arie Zigler
- Optics letters
- 2004

In this Letter we provide what is believed to be the first experimental evidence of suppression of the number of filaments for high-intensity laser pulses propagating in air by beam astigmatism. We also show that the number, pattern, and spatial stability of the filaments can be controlled by varying the angle that a focusing lens makes with the axial… (More)

- Audrius Dubietis, Gintaras Tamosauskas, Gadi Fibich, Boaz Ilan
- Optics letters
- 2004

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)

- Mark J Ablowitz, Boaz Ilan, Ethan Schonbrun, Rafael Piestun
- Physical review. E, Statistical, nonlinear, and…
- 2006

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)