# Accelerated Rogue Solitons Triggered by Background Radiation

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• Waves on Deep Water, I
Lecture 14: Waves on deep water, I Lecturer: Harvey Segur. Write-up: Adrienne Traxler June 23, 2009 1 Introduction In this lecture we address the question of whether there are stable wave patterns that propagate with permanent (or nearly permanent) form on deep water. The primary tool for this investigation is the nonlinear Schr¨odinger equation (NLS). Below we sketch the derivation of the NLS for deep water waves, and review earlier work on the existence and stability of 1D surface patterns for these waves. The next lecture continues to more recent work on 2D surface patterns and the eﬀect of adding small damping. 2 Derivation of NLS for deep water waves The nonlinear Schr¨odinger equation (NLS) describes the slow evolution of a train or packet of waves with the following assumptions: • the system is conservative (no dissipation) • then the waves are dispersive (wave speed depends on wavenumber) Now examine the subset of these waves with • only small or moderate amplitudes • traveling in nearly the same direction • with nearly the same frequency The derivation sketch follows the by now normal procedure of beginning with the water wave equations, identifying the limit of interest, rescaling the equations to better show that limit, then solving order-by-order. We begin by considering the case of only gravity waves (neglecting surface tension), in the deep water limit (kh → ∞). Here h is the distance between the equilibrium surface height and the (ﬂat) bottom; a is the wave amplitude; η is the displacement of the water surface from the equilibrium level; and φ is the velocity potential, u = ∇φ.
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• 21 Non-Linear Wave Equations and Solitons
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• Shallow Water Waves and Solitary Waves Article Outline Glossary
Shallow Water Waves and Solitary Waves Willy Hereman Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, USA Article Outline Glossary I. Deﬁnition of the Subject II. Introduction{Historical Perspective III. Completely Integrable Shallow Water Wave Equations IV. Shallow Water Wave Equations of Geophysical Fluid Dynamics V. Computation of Solitary Wave Solutions VI. Water Wave Experiments and Observations VII. Future Directions VIII. Bibliography Glossary Deep water A surface wave is said to be in deep water if its wavelength is much shorter than the local water depth. Internal wave A internal wave travels within the interior of a ﬂuid. The maximum velocity and maximum amplitude occur within the ﬂuid or at an internal boundary (interface). Internal waves depend on the density-stratiﬁcation of the ﬂuid. Shallow water A surface wave is said to be in shallow water if its wavelength is much larger than the local water depth. Shallow water waves Shallow water waves correspond to the ﬂow at the free surface of a body of shallow water under the force of gravity, or to the ﬂow below a horizontal pressure surface in a ﬂuid. Shallow water wave equations Shallow water wave equations are a set of partial diﬀerential equations that describe shallow water waves. 1 Solitary wave A solitary wave is a localized gravity wave that maintains its coherence and, hence, its visi- bility through properties of nonlinear hydrodynamics. Solitary waves have ﬁnite amplitude and propagate with constant speed and constant shape. Soliton Solitons are solitary waves that have an elastic scattering property: they retain their shape and speed after colliding with each other.
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• Soliton and Some of Its Geophysical/Oceanographic Applications
Introduction Historical KdV equation Other equations Theory Applications Higher dimensions Problems Soliton and Some of its Geophysical/Oceanographic Applications M. Lakshmanan Centre for Nonlinear Dynamics Bharathidasan University Tiruchirappalli – 620024 India Discussion Meeting, ICTS-TIFR 21 July 2016 M. Lakshmanan Soliton and Some of its Geophysical Introduction Historical KdV equation Other equations Theory Applications Higher dimensions Problems Theme Soliton is a counter-intuitive wave entity arising because of a delicate balance between dispersion and nonlinearity. Its major attraction is its localized nature, ﬁnite energy and preservation of shape under collision = a remark- ably stable structure. Consequently, it has⇒ ramiﬁcations in as wider areas as hydrodynamics, tsunami dynamics, condensed matter, magnetism, particle physics, nonlin- ear optics, cosmology and so on. A brief overview will be presented with emphasis on oceanographic applications and potential problems will be indicated. M. Lakshmanan Soliton and Some of its Geophysical Introduction Historical KdV equation Other equations Theory Applications Higher dimensions Problems Plan 1 Introduction 2 Historical: (i) Scott-Russel (ii) Zabusky/Kruskal 3 Korteweg-de Vries equation and solitary wave/soliton 4 Other ubiquitous equations 5 Mathematical theory of solitons 6 Geophysical/Oceanographic applications 7 Solitons in higher dimensions 8 Problems and potentialities M. Lakshmanan Soliton and Some of its Geophysical Introduction Historical KdV equation Other equations Theory
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• High-Throughput Biological Cell Classification Featuring Real-Time Optical Data Compression
Conference on Information Sciences and Systems, CISS 2015, Baltimore, MD, USA, March 18-20 2015 High-throughput Biological Cell Classification Featuring Real-time Optical Data Compression Bahram Jalali*, Ata Mahjoubfar, and Claire L. Chen Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA Plenary Talk *Email: [email protected] Abstract—High throughput real-time instruments are needed the current gold standard in high-speed fluorescence imaging to acquire large data sets for detection and classification of rare [16]. events. Enabled by the photonic time stretch digitizer, a new class of instruments with record throughputs have led to the discovery Producing data rates as high as one tera bit per second, of optical rogue waves [1], detection of rare cancer cells [2], and these real-time instruments pose a big data challenge that the highest analog-to-digital conversion performance ever overwhelms even the most advanced computers [17]. Driven achieved [3]. Featuring continuous operation at 100 million by the necessity of solving this problem, we have recently frames per second and shutter speed of less than a nanosecond, introduced and demonstrated a categorically new data the time stretch camera is ideally suited for screening of blood compression technology [18, 19]. The so called Anamorphic and other biological samples. It has enabled detection of breast (warped) Stretch Transform is a physics based data processing cancer cells in blood with record, one-in-a-million, sensitivity [2]. technique that aims to mitigate the big data problem in real- Owing to their high real-time throughput, instruments produce a time instruments, in digital imaging, and beyond [17-21].
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• Dissipative Cnoidal Waves (Turing Rolls) and the Soliton Limit in Microring Resonators
Research Article Vol. X, No. X / Febrary 1046 B.C. / OSA Journal 1 Dissipative cnoidal waves (Turing rolls) and the soliton limit in microring resonators ZHEN QI1,*,S HAOKANG WANG1,J OSÉ JARAMILLO-VILLEGAS2,M INGHAO QI3, ANDREW M. WEINER3,G IUSEPPE D’AGUANNO1,T HOMAS F. CARRUTHERS1, AND CURTIS R. MENYUK1 1University of Maryland at Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA 2Technological University of Pereira, Cra. 27 10-02, Pereira, Risaralda 660003, Colombia 3Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA *Corresponding author: [email protected] Compiled May 27, 2019 Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and acces- sibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter space that consists of detuning, pump amplitude, and mode cir- cumference in order to determine where stable solutions exist. To carry out this task, we use a unique set of computational tools based on dynamical system theory that allow us to rapidly and accurately determine the stable region for each cnoidal wave periodicity and to ﬁnd the instabil- ity mechanisms and their time scales. Finally, we focus on the soliton limit, and we show that the stable region for single solitons almost completely overlaps the stable region for both con- tinuous waves and several higher-periodicity cnoidal waves that are effectively multiple soliton trains.
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• Dissipative Rogue Waves Generated by Chaotic Pulse Bunching in a Mode-Locked Laser
week ending PRL 108, 233901 (2012) PHYSICAL REVIEW LETTERS 8 JUNE 2012 Dissipative Rogue Waves Generated by Chaotic Pulse Bunching in a Mode-Locked Laser C. Lecaplain,1 Ph. Grelu,1 J. M. Soto-Crespo,2 and N. Akhmediev3 1Laboratoire Interdisciplinaire Carnot de Bourgogne, U.M.R. 6303 C.N.R.S., Universite´ de Bourgogne, 9 avenue A. Savary, BP 47870 Dijon Cedex 21078, France 2Instituto de O´ ptica, C.S.I.C., Serrano 121, 28006 Madrid, Spain 3Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia (Received 14 December 2011; published 5 June 2012) Rare events of extremely high optical intensity are experimentally recorded at the output of a mode- locked ﬁber laser that operates in a strongly dissipative regime of chaotic multiple-pulse generation. The probability distribution of these intensity ﬂuctuations, which highly depend on the cavity parameters, features a long-tailed distribution. Recorded intensity ﬂuctuations result from the ceaseless relative motion and nonlinear interaction of pulses within a temporally localized multisoliton phase. DOI: 10.1103/PhysRevLett.108.233901 PACS numbers: 42.65.Tg, 47.20.Ky Waves of extreme amplitude, or ‘‘rogue waves,’’ have satisfying the criteria of rogue waves [17,18]. In order to been the subject of intense research activity during the past strongly interact, the multiplicity of pulses should be con- decade [1,2]. Initiated ﬁrst in the context of oceanic waves, ﬁned within a relatively tight temporal domain. The two where the induced stakes and consequences are the most predictions also stressed the dominant impact of dissipa- critical, the notion of ‘‘rogue waves’’ or ‘‘freak waves’’ is tive effects on the involved nonlinear dynamics.
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• The Universal Route to Rogue Waves
PHYSICAL REVIEW X 9, 041057 (2019) Featured in Physics Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves Giovanni Dematteis ,1,2 Tobias Grafke,3 Miguel Onorato ,2,4 and Eric Vanden-Eijnden5 1Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy 2Dipartimento di Fisica, Universit`a degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy 3Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom 4INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy 5Courant Institute, New York University, 251 Mercer Street, New York, New York 10012, USA (Received 3 July 2019; revised manuscript received 2 October 2019; published 18 December 2019) A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatiotemporal wave field configurations which can be defined using the mathematical framework of large deviation theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves created by simple linear superposition (in weakly nonlinear conditions) or by nonlinear focusing (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation. DOI: 10.1103/PhysRevX.9.041057 Subject Areas: Fluid Dynamics, Nonlinear Dynamics, Statistical Physics I.
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• Three-Dimensional Dynamics of Baroclinic Tides Over a Seamount
University of Plymouth PEARL https://pearl.plymouth.ac.uk Faculty of Science and Engineering School of Biological and Marine Sciences 2018-02 Three-dimensional dynamics of baroclinic tides over a seamount Vlasenko, V http://hdl.handle.net/10026.1/10845 10.1002/2017JC013287 Journal of Geophysical Research: Oceans American Geophysical Union All content in PEARL is protected by copyright law. Author manuscripts are made available in accordance with publisher policies. Please cite only the published version using the details provided on the item record or document. In the absence of an open licence (e.g. Creative Commons), permissions for further reuse of content should be sought from the publisher or author. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1002/, Three-dimensional dynamics of baroclinic tides over a seamount 1 1 1 Vasiliy Vlasenko , Nataliya Stashchuk , and W. Alex M. Nimmo-Smith Vasiliy Vlasenko, School of Biological and Marine Sciences, Plymouth University, Plymouth, PL4 8AA, UK ([email protected]) 1School of Biological and Marine Sciences, Plymouth University, Plymouth, PL4 8AA, UK. D R A F T January 17, 2018, 10:45am D R A F T X-2 VLASENKO ET AL.: BAROCLINIC TIDES OVER A SEAMOUNT 1 Abstract. 2 The Massachusetts Institute of Technology general circulation model is used 3 for the analysis of baroclinic tides over Anton Dohrn Seamount (ADS), in 4 the North Atlantic. The model output is validated against in-situ data col- 5 lected during the 136-th cruise of the RRS “James Cook” in May-June 2016. 6 The observational data set includes velocity time series recorded at two moor- 7 ings as well as temperature, salinity and velocity proﬁles collected at 22 hy- 8 drological stations.
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• Optical Rogue Wave in Random Distributed Feedback Fiber Laser Jiangming Xu1,2, Jian Wu1,2, Jun Ye1, Pu Zhou1,2,*, Hanwei Zhang1,2, Jiaxin Song1, & Jinyong Leng1,2
Optical rogue wave in random distributed feedback fiber laser Jiangming Xu1,2, Jian Wu1,2, Jun Ye1, Pu Zhou1,2,*, Hanwei Zhang1,2, Jiaxin Song1, & Jinyong Leng1,2 The famous demonstration of optical rogue wave (RW)-rarely and unexpectedly event with extremely high intensity-had opened a flourishing time for temporal statistic investigation as a powerful tool to reveal the fundamental physics in different laser scenarios. However, up to now, optical RW behavior with temporally localized structure has yet not been presented in random fiber laser (RFL) characterized with mirrorless open cavity, whose feedback arises from distinctive distributed multiple scattering. Here, thanks to the participation of sustained and crucial stimulated Brillouin scattering (SBS) process, experimental explorations of optical RW are done in the highly-skewed transient intensity of an incoherently-pumped standard-telecom-fiber-constructed RFL. Furthermore, threshold-like beating peak behavior can also been resolved in the radiofrequency spectroscopy. Bringing the concept of optical RW to RFL domain without fixed cavity may greatly extend our comprehension of the rich and complex kinetics such as photon propagation and localization in disordered amplifying media with multiple scattering. 1 College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China . 2 Hunan Provincial Collaborative Innovation Center of High Power Fiber Laser, Changsha 410073, China. J. X. and J. W. contributed equally to this paper. Correspondence and requests for materials should be addressed to P. Z. (email: [email protected]). The concept of random laser employing multiple scattering of photons in an amplifying disordered material to achieve coherent light has attracted increasing attention due to its special features, such as cavity-free, structural simplicity, and promising applications in imaging, medical diagnostics, and other scientific or industrial fields [1-3].
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• Plasmon-Soliton
Plasmon-Soliton Eyal Feigenbaum and Meir Orenstein Department of Electrical Engineering, Technion, Haifa 32000, Israel [email protected] Abstract : Formation of a novel hybrid-vector spatial plasmon-soliton in a Kerr slab embedded in-between metal plates is predicted and analyzed with a modified NLSE, encompassing hybrid vector field characteristics. Assisted by the transverse plasmonic effect, the self trapping dimension of the plasmon-soliton was substantially compressed (compared to the dielectrically cladded slab case) when reducing the slab width. The practical limitation of the Plasmon-soliton size reduction is determined by available nonlinear materials and metal loss. For the extreme reported values of nonlinear index change, we predict soliton with a cross section of 300nm×30nm (average dimension of 100nm). 1 The downscaling of conventional photonics is halted when approaching a transverse dimension of ~ λ/2 ( λ is the wavelength). This limitation can be alleviated by the incorporation of metals, giving rise to surface plasmon polaritons (SPP) [1,2]. Here we analyze a novel configuration where light is transversely tightly guided between two metal layers, and laterally self trapped by a nonlinear Kerr effect to yield a plasmon-soliton. The tight field confinement of this scheme is important for potential excitation of plasmon-solitons by a low power continuous wave optical source, which is further assisted by the expected small group velocity of the plasmon-soliton. In this letter we present for the first time both an analysis of TM spatial solitons, using the Non- linear Schrödinger Equation (NLSE), where the full vectorial field is considered, as well as the prediction and characteristics of SPP based solitons.
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• Soliton and Rogue Wave Statistics in Supercontinuum Generation In
Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths Bertrand Kibler, Christophe Finot, John M. Dudley To cite this version: Bertrand Kibler, Christophe Finot, John M. Dudley. Soliton and rogue wave statistics in supercon- tinuum generation in photonic crystal fibre with two zero dispersion wavelengths. The European Physical Journal. Special Topics, EDP Sciences, 2009, 173 (1), pp.289-295. 10.1140/epjst/e2009- 01081-y. hal-00408633 HAL Id: hal-00408633 https://hal.archives-ouvertes.fr/hal-00408633 Submitted on 17 Apr 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. EPJ manuscript No. (will be inserted by the editor) Soliton and rogue wave statistics in supercontinuum generation in photonic crystal ¯bre with two zero dispersion wavelengths Bertrand Kibler,1 Christophe Finot1 and John M. Dudley2 1 Institut Carnot de Bourgogne, UMR 5029 CNRS-Universit¶ede Bourgogne, 9 Av. A. Savary, Dijon, France 2 Institut FEMTO-ST, UMR 6174 CNRS-Universit¶ede Franche-Comt¶e,Route de Gray, Besan»con, France. Abstract. Stochastic numerical simulations are used to study the statistical prop- erties of supercontinuum spectra generated in photonic crystal ¯bre with two zero dispersion wavelengths.
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