Multiple fragmentation of wave packets in a nonlinear medium with normal dispersion of the group velocity

Litvak, A. G.; Миронов, В. А.; Sher, E. M.

doi:10.1134/1.1342895

Cited by 4 publications

(6 citation statements)

References 11 publications

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“…Based on our numerical findings the universal regime with a central hyperbolic structure eventually develops even for initial lumps of relatively large amplitude. We believe that the phenomena discussed in literature like spiky hyperbolic structures numerically observed in [32,12,13,55,56] as well as observed X-waves [15,16,17,36,30] correspond to intermediate regimes just at the onset of the hyperbolic long-time asymptotic structure, at least in the (2+1)-D case considered here. We expect these waves to eventually develop into the universal regime, perhaps with many centers as we also observed in our simulations.…”

Section: Discussion Of the Resultssupporting

confidence: 65%

“…For relatively small initial amplitudes, the reshaping of the wave packet can be well described by considering nonlinearity as a perturbation to the linearized equation. This way one can quantitatively understand the dumbbell shapes often observed forming from the initial round beam both in two and three spatial dimensions [33,34,32,12,1]. We analyzed this situation in section 2 for an initial Gaussian beam and showed, as expected, that the beam is compressed in the focusing x-direction and decompressed in the defocusing y-direction.…”

Section: Discussion Of the Resultsmentioning

confidence: 79%

“…Previous numerical investigations, e.g. [10,12,32], also found that for larger initial amplitudes of HNLS high resolutions are required to obtain reliable results. In this work we do not investigate large or rapidly varying functions.…”

Section: Discussion Of the Resultsmentioning

confidence: 97%

“…Apart from analyzing the development of instabilities of one-dimensional solutions [25,26,27], there has been some numerical and experimental research on the HNLS equation [33,46,42,32,13,36,30]. There has also been a number of studies of the (3+1)-D HNLS eq., see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…such as pulse splitting, multi-filamentation, fragmentation, so-called snake and neck instabilities and nonlinear X-waves, have qualitative counterparts in the HNLS eq. [32,12,13,25,30,26,27].…”

Section: Introductionmentioning

confidence: 99%

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A Universal Asymptotic Regime in the Hyperbolic Nonlinear Schrödinger Equation

Ablowitz¹,

Ma²,

Rumanov³

2017

SIAM J. Appl. Math.

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The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schrödinger (HNLS) equation is discussed. Based on analytical and extensive numerical simulations an approximate self-similar solution is found for a wide range of initial conditions -essentially for initial lumps of small to moderate energy. Even relatively large initial amplitudes, which imply strong nonlinear effects, eventually lead to local structures resembling those of the self-similar solution, with appropriate small modifications. These modifications are important in order to properly capture the behavior of the phase of the solution. This solution has aspects that suggest it is a universal attractor emanating from wide ranges of initial data.

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Section: Discussion Of the Resultssupporting

confidence: 65%

Section: Discussion Of the Resultsmentioning

confidence: 79%

Section: Discussion Of the Resultsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Universal Asymptotic Regime in the Hyperbolic Nonlinear Schrödinger Equation

Ablowitz¹,

Ma²,

Rumanov³

2017

SIAM J. Appl. Math.

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Numerical Computations

Trott

2006

The Mathematica GuideBook for Numerics

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Ultrashort filaments of light in weakly ionized, optically transparent media

et al. 2007

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Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration and peak powers exceeding several terawatt (TW). When such pulses propagate through optically transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium and the defocusing action of the electron plasma. Discovered one decade ago, this self-channeling mechanism reveals a new physics, widely extending the frontiers of nonlinear optics. Implications include long-distance propagation of TW beams in the atmosphere, supercontinuum emission, pulse shortening as well as high-order harmonic generation. This review presents the landmarks of the 10-odd-year progress in this field. Particular emphasis is laid on the theoretical modeling of the propagation equations, whose physical ingredients are discussed from numerical simulations. The dynamics of single filaments created over laboratory scales in various materials such as noble gases, liquids and dielectrics reveal new perspectives in pulse shortening techniques. Far-field spectra provide promising diagnostics. Attention is also paid to the multifilamentation instability of broad beams, breaking up the energy distribution into small-scale cells along the optical path. The robustness of the resulting filaments in adverse weathers, their large conical emission exploited for multipollutant remote sensing, nonlinear spectroscopy and the possibility of guiding electric discharges in air are finally addressed on the basis of experimental results.

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Multiple fragmentation of wave packets in a nonlinear medium with normal dispersion of the group velocity

Cited by 4 publications

References 11 publications

A Universal Asymptotic Regime in the Hyperbolic Nonlinear Schrödinger Equation

A Universal Asymptotic Regime in the Hyperbolic Nonlinear Schrödinger Equation

Numerical Computations

Ultrashort filaments of light in weakly ionized, optically transparent media

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