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Dynamics and stabilization of bright soliton stripes in the hyperbolic-dispersion nonlinear Schrödinger equation

L.A. Cisneros-Ake, R. Carretero-González, P.G. Kevrekidis, B.A. Malomed
2019 Communications in nonlinear science & numerical simulation  
We consider the dynamics and stability of bright soliton stripes in the two-dimensional nonlinear Schr\"odinger equation with hyperbolic dispersion, under the action of transverse perturbations.  ...  We then focus on a variational approximation used to reduce the dynamics of the bright-soliton stripe to effective equations of motion for its transverse shift.  ...  Acknowledgements LACA gratefully acknowledges the leave absence permit from IPN and the financial support of the Fulbright-García Robles program during his research stay at SDSU.  ... 
doi:10.1016/j.cnsns.2019.03.012 fatcat:4poeck2v4ncndcojkaakwvfdvm

Neck instability of bright solitons in normally dispersive Kerr media

Simon-Pierre Gorza, Bernard Deconinck, Thomas Trogdon, Philippe Emplit, Marc Haelterman
2012 Optics Letters  
The neck instability of bright solitons of the hyperbolic nonlinear Shrödinger equation is investigated.  ...  In particular, for the case of focusing Kerr nonlinearity, the dynamics is governed by the nonlinear Schrödinger (NLS) equation that possesses solutions in the form of bright (1+1)D spatial solitons.  ...  Let us consider the hyperbolic nonlinear Schrödinger equation with normal time dispersion: i ∂ψ ∂Z + 1 2 ∂ 2 ψ ∂X 2 − 1 2 ∂ 2 ψ ∂T 2 + |ψ| 2 ψ = 0. (1) In optics, this equation describes the dynamics of  ... 
doi:10.1364/ol.37.004657 pmid:23164870 fatcat:hqwc63mdpfcvrjygk5z3gglfra

Suppression of transverse instabilities of dark solitons and their dispersive shock waves

Andrea Armaroli, Stefano Trillo, Andrea Fratalocchi
2009 Physical Review A. Atomic, Molecular, and Optical Physics  
The nonlocal response turns out to have a strongly stabilizing effect both in the case of a single soliton input and in the regime where dispersive shock waves develop "multisoliton regime".  ...  Such conclusions are supported by the linear stability analysis and numerical simulation of the propagation.  ...  In particular, for the case of defocusing or repulsive Kerr-like (cubic) nonlinearities where the dynamics is governed by the equations of the nonlinear Schrödinger (NLS) type in two transverse dimensions  ... 
doi:10.1103/physreva.80.053803 fatcat:wlm6ahyfnrbmzdtvx6jxew3mw4

Stability analysis of spatiotemporal cnoidal waves in cubic nonlinear media

Victor A. Aleshkevich, Alexey A. Egorov, Yaroslav V. Kartashov, Victor A. Vysloukh, Anna S. Zelenina
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We analyze numerically the modulational instability of spatiotemporal cnoidal waves of cn, dn, and sn types that are periodic along a single space coordinate and are uniform in time.  ...  It is shown that this band transforms into a set of discrete values for waves of cn and dn types in the limit of strong spatial localization.  ...  ACKNOWLEDGMENTS The authors acknowledge financial support from RFBR under Grant No. 03-02-16370 and from CONACYT under Grant No. 34684-E. The work of Yaroslav V.  ... 
doi:10.1103/physreve.67.066605 pmid:16241366 fatcat:vqaszo35tvarrofsto5sw4z5ry

Observation of a Gradient Catastrophe Generating Solitons

Claudio Conti, Andrea Fratalocchi, Marco Peccianti, Giancarlo Ruocco, Stefano Trillo
2009 Physical Review Letters  
We investigate the propagation of a dark beam in a defocusing medium in the strong nonlinear regime.  ...  Remarkably this scenario turns out to be very robust, persisting also when the material nonlocal response averages the nonlinearity over dimensions much larger than the emerging soliton filaments.  ...  The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013)/ERC grant agreement n. 201766.  ... 
doi:10.1103/physrevlett.102.083902 pmid:19257740 fatcat:sccszo2wyncuniurc27234zjym

Three-Dimensional Vortex Solitons in Self-Defocusing Media

Nikolaos K. Efremidis, Kyriakos Hizanidis, Boris A. Malomed, Paolo Di Trapani
2007 Physical Review Letters  
We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schrödinger equation.  ...  These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity.  ...  We demonstrate that 3D vortices exist in media with the cubic defocusing nonlinearity and normal group velocity dispersion (GVD), i.e., the diffraction-dispersion operator is of the hyperbolic type.  ... 
doi:10.1103/physrevlett.98.113901 pmid:17501055 fatcat:c7e74mo7avcpdlpduvwtht2rue

Three-dimensional vortex solitons in self-defocusing media [article]

Nikolaos K. Efremidis, Kyriakos Hizanidis, Boris A. Malomed, Paolo Di Trapani
2007 arXiv   pre-print
We demonstrate that families of vortex solitons are possible in a bi-dispersive three-dimensional nonlinear Schrodinger equation.  ...  These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity.  ...  We demonstrate that 3D vortices exist in media with the cubic defocusing nonlinearity and normal GVD (group velocity dispersion), i.e., the diffraction-dispersion operator is of the hyperbolic type.  ... 
arXiv:nlin/0703021v1 fatcat:2eszmdcw3re4jd7ywd5dvunnpa

Spectral transverse instabilities and soliton dynamics in the higher-order multidimensional nonlinear Schrödinger equation

Justin T. Cole, Ziad H. Musslimani
2015 Physica D : Non-linear phenomena  
The time dynamics of a one-dimensional soliton stripe in the presence of a transverse perturbation is studied using direct numerical simulations.  ...  Spectral transverse instabilities of one-dimensional solitary wave solutions to the two-dimensional nonlinear Schrödinger (NLS) equation with fourth-order dispersion/diffraction subject to higher-dimensional  ...  Our model equation is the two-dimensional nonlinear Schrödinger equation in the presence of a fourth-order dispersion/diffraction.  ... 
doi:10.1016/j.physd.2015.09.005 fatcat:soxsz6s6yzhirjpwbrfeiavvzi

Editorial (a preface to a Special Issue of journal Applied Sciences on "Guided-Wave Optics") [article]

Boris A. Malomed
2017 arXiv   pre-print
The Special Issue is a collection of 20 original and review articles dealing with various fundamental and applied aspects of the topic.  ...  This is a preface introducing a Special Issue on the topic of "Guided-Wave Optics" published by Applied Sciences.  ...  Kevrekidis, and Peter Schmelcher, Stability and Dynamics of Dark-Bright Soliton Bound States Away from the Integrable Limit, Appl. Sci. 7, 388 (2017); (B3) P. Rodriguez, J. Jimenez, T.  ... 
arXiv:1709.05518v1 fatcat:rqetqvcouresxeo5aextpwytlu

Wave envelopes with second-order spatiotemporal dispersion. I. Bright Kerr solitons and cnoidal waves

J. M. Christian, G. S. McDonald, T. F. Hodgkinson, P. Chamorro-Posada
2012 Physical Review A. Atomic, Molecular, and Optical Physics  
The generic governing equation has a cubic nonlinearity, and we focus here mainly on contexts involving anomalous group-velocity dispersion.  ...  Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of predictions is made.  ...  Space-time geometry of solitons The forward-propagating soliton must form a stripe in the (τ ,ζ ) plane that spans the first and third quadrants.  ... 
doi:10.1103/physreva.86.023838 fatcat:pquqjtby7rbyhn73g5kvbky2se

Reduced dynamics for one and two dark soliton stripes in the defocusing nonlinear Schrödinger equation: A variational approach

L. A. Cisneros-Ake, R. Carretero-González, P. G. Kevrekidis
2019 Physical Review Research  
We study the dynamics and pairwise interactions of dark soliton stripes in the two-dimensional defocusing nonlinear Schr\"odinger equation.  ...  By employing a variational approach we reduce the dynamics for dark soliton stripes to a set of coupled one-dimensional "filament" equations of motion for the position and velocity of the stripe.  ...  also quantitatively match more adequately the dispersion curves and consequently the nonlinear dynamics of the solitonic stripes.  ... 
doi:10.1103/physrevresearch.1.033043 fatcat:tzqpz6uvxvhslp6rypjxrownni

Editorial: Guided-Wave Optics

Boris Malomed
2017 Applied Sciences  
The text is structured according to the character of the guided wave propagation: linear or nonlinear and conservative or dissipative, as well as according to the materials used in the underlying settings  ...  Arguably, the most well-known and practically important waveguides are single-mode and multi-mode optical fibers [1,2], including their more sophisticated version in the form of photonic crystal fibers  ...  Stability and Dynamics of Dark-Bright Soliton Bound States Away from the Integrable Limit. Appl. Sci. 2017, 7, 388. (B3) Rodriguez, P.; Jimenez, J.; Guillet, T.; Ackemann, T.  ... 
doi:10.3390/app7090962 fatcat:qya4zvfzrnezhmtu53i2mtwqbu

Bright and dark solitary waves in the presence of third-harmonic generation

Rowland A. Sammut, Alexander V. Buryak, Yuri S. Kivshar
1998 Journal of the Optical Society of America. B, Optical physics  
We analyze the effect of phase-matched third-harmonic generation on the existence and stability of (1 ϩ 1)-dimensional bright and dark spatial solitary waves in optical media with a cubic (or Kerr) nonlinear  ...  In particular, we find a power threshold for the existence of two-frequency parametric bright solitons and also reveal the soliton multistability in a Kerr medium that becomes possible owing to a higher-order  ...  Schrödinger (NLS) equation 11 we expect that solitary waves cease to exist when the effective quintic nonlinearity becomes strongly defocusing.  ... 
doi:10.1364/josab.15.001488 fatcat:ivikl4lbdbb4xdzdtedwks26ce

Transversely stable soliton trains in photonic lattices

Jianke Yang
2011 Physical Review A. Atomic, Molecular, and Optical Physics  
We report the existence of transversely stable soliton trains in optics.  ...  We also show that soliton trains with low amplitudes or bifurcated from edges of the first Bloch band (Gamma and M points) still suffer transverse instability.  ...  ACKNOWLEDGMENTS This work is supported in part by the Air Force Office of Scientific Research (Grant USAF 9550-09-1-0228) and the National Science Foundation (Grant DMS-0908167).  ... 
doi:10.1103/physreva.84.033840 fatcat:kq2dct4ylzdmli2gwrgssreezu

All-optical discrete vortex switch

Anton S. Desyatnikov, Mark R. Dennis, Albert Ferrando
2011 Physical Review A. Atomic, Molecular, and Optical Physics  
We introduce discrete vortex solitons and vortex breathers in circular arrays of nonlinear waveguides.  ...  The simplest vortex breather in a four-waveguide coupler is a nonlinear dynamic state changing its topological charge between +1 and −1 periodically during propagation.  ...  MODEL AND SOLITON SOLUTIONS We begin with the discrete nonlinear Schrödinger equation governing the propagation of light in weakly coupled waveguides with Kerr nonlinearity [25, 26] : (1) where δ =  ... 
doi:10.1103/physreva.83.063822 fatcat:ynwiqrjx2rds3e5coqsfpgb4zi
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