Dynamical Evolution of Sasa–Satsuma Rogue Waves, Breather Solutions, and New Special Wave Phenomena in a Nonlinear Metamaterial

2020 ◽  
pp. 2000316
Author(s):  
Bedel Giscard Onana Essama ◽  
Salome Ndjakomo Essiane ◽  
Frederic Biya-Motto ◽  
Bibiane Mireille Ndi Nnanga ◽  
Mohammed Shabat ◽  
...  
Keyword(s):  
Dynamical Evolution ◽  
Rogue Waves ◽  
Wave Phenomena ◽  
Nonlinear Metamaterial

Optical rogue waves generation in a nonlinear metamaterial

2014 ◽  
Vol 331 ◽  
pp. 334-347 ◽  
Author(s):  
Bedel Giscard Onana Essama ◽  
Jacques Atangana ◽  
Frederick Biya-Motto ◽  
Bouchra Mokhtari ◽  
Noureddine Cherkaoui Eddeqaqi ◽  
...  
Keyword(s):  
Rogue Waves ◽  
Nonlinear Metamaterial

Breathers, rogue waves and their dynamics in a (2+1)-dimensional nonlinear Schrödinger equation

2020 ◽  
Vol 34 (23) ◽  
pp. 2050234
Author(s):  
Yong Chen ◽  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Plane Wave Solution ◽  
Nonlinear Schrödinger ◽  
Wave Phenomena

Under investigation in this paper is a (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger equation, which is a generalization of the standard nonlinear Schrödinger equation. By means of the modified Darboux transformation, the hierarchies of rational solutions and breather solutions are generated from the plane wave solution. Furthermore, the main characteristics of the nonlinear waves including the Akhmediev breathers, Kuznetsov–Ma solitons, and their combined structures are graphically discussed. Our results would be of much importance in enriching and explaining rogue wave phenomena in nonlinear wave fields.

Inverse scattering method for the Kundu-Eckhaus equation with zero/nonzero boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Guixian Wang ◽  
Xiu-Bin Wang ◽  
Bo Han ◽  
Qi Xue
Keyword(s):  
Boundary Conditions ◽  
Inverse Scattering ◽  
Hilbert Problem ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Higher Order ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Nonzero Boundary ◽  
Wave Phenomena

Abstract In this paper, the inverse scattering approach is applied to the Kundu-Eckhaus equation with two cases of zero boundary condition (ZBC) and nonzero boundary conditions (NZBCs) at infinity. Firstly, we obtain the exact formulae of soliton solutions of three cases of N simple poles, one higher-order pole and multiple higher-order poles via the associated Riemann-Hilbert problem (RHP). Moreover, given the initial data that allow for the presence of discrete spectrum, the higher-order rogue waves of the equation are presented. For the case of NZBCs, we can construct the infinite order rogue waves through developing a suitable RHP. Finally, by choosing different parameters, we aim to show some prominent characteristics of this solution and express them graphically in detail. Our results should be helpful to further explore and enrich the related nonlinear wave phenomena.

scholarly journals Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

2021 ◽  
Vol 9 (6) ◽  
pp. 577
Author(s):  
Qing Pan ◽  
Hui-Min Yin ◽  
Kwok W. Chow
Keyword(s):  
Internal Waves ◽  
Plane Waves ◽  
Wave Spectrum ◽  
Dynamical Evolution ◽  
Rogue Waves ◽  
Wave Mode ◽  
Transport Processes ◽  
Buoyancy Frequency ◽  
Extreme Waves ◽  
Surface Gravity Wave

Internal waves in a stratified fluid with a constant buoyancy frequency were studied, with special attention given to rogue modes, extreme waves, dynamical evolution, and Fermi–Pasta–Ulam–Tsingou type recurrence phenomena. Rogue waves for triads in a general physical setting have recently been derived analytically, but the implications in a fluid mechanics context have not yet been fully assessed. Numerical simulations were conducted for cases of coupled triads where the common member is a daughter wave mode. In sharp contrast with previous studies, rogue modes instead of plane waves were used as the initial condition. Furthermore, spatial dependence was incorporated. Rogue or extreme waves in one set of triads provided a possible mechanism for significant energy transfer among modes of the internal wave spectrum, in addition to the other known theories, e.g., weak turbulence. Remarkably, Fermi–Pasta–Ulam–Tsingou recurrence types of growth and decay cycles arose, similarly to those observed for surface gravity wave groups governed by the cubic nonlinear Schrödinger equation. These mechanisms will enhance our understanding of transport processes in oceans.

The Velocity Field Underneath Linear and Nonlinear Breaking Rogue Waves

2016 ◽  
Author(s):  
Alberto Alberello ◽  
Amin Chabchoub ◽  
Alexander V. Babanin ◽  
Jason P. Monty ◽  
John Elsnab ◽  
...  
Keyword(s):  
Velocity Field ◽  
Field Experiments ◽  
Dynamical Evolution ◽  
Wave Theory ◽  
Rogue Waves ◽  
Breaking Waves ◽  
New Wave ◽  
Image Velocimetry ◽  
Surface Measurements ◽  
The University

During the past decades, a large number of waves of extreme height and abnormal shape, also known as freak or rogue waves, have been recorded in the ocean. Velocities and related forces can be enormous and jeopardise the safety of marine structures. Here, we present an experimental study devoted to investigate the velocity field underneath a breaking rogue wave. The latter is replicated in the laboratory by means of dispersive focussing methods such as the New Wave Theory and nonlinear focussing techniques based on the Nonlinear Schrödinger equation. While the former is basically a liner method, the nonlinear focussing fully accounts for the dynamical evolution of the wave field. Experiments were carried out in the Extreme Air-Sea Interaction flume of the University of Melbourne using a Particle Image Velocimetry (PIV) system to measure the velocity field below the water surface. Measurements show that the mechanism of generation affects the shape of the breaking waves as well as the kinematic field and associated hydrodynamic forces. Particularly, the New Wave Theory leads to higher velocities and a more energetic breaker than the nonlinear focussing.

Statistical results on discovered near-Earth asteroids

1999 ◽  
Vol 173 ◽  
pp. 81-86
Author(s):  
S. Berinde
Keyword(s):  
Dynamical Evolution ◽  
Minor Planet ◽  
Orbital Elements ◽  
The Earth ◽  
Near Earth Asteroids ◽  
Statistical Results

AbstractThe first part of this paper gives a recent overview (until July 1st, 1998) of the Near-Earth Asteroids (NEAs) database stored at Minor Planet Center. Some statistical interpretations point out strong observational biases in the population of discovered NEAs, due to the preferential discoveries, depending on the objects’ distances and sizes. It is known that many newly discovered NEAs have no accurately determinated orbits because of the lack of observations. Consequently, it is hard to speak about future encounters and collisions with the Earth in terms of mutual distances between bodies. Because the dynamical evolution of asteroids’ orbits is less sensitive to the improvement of their orbital elements, we introduced a new subclass of NEAs named Earth-encounter asteroids in order to describe more reliably the potentially dangerous bodies as impactors with the Earth. So, we pay attention at those asteroids having an encounter between their orbits and that of the Earth within 100 years, trying to classify these encounters.

From the Oort cloud to Halley-type comets

1999 ◽  
Vol 173 ◽  
pp. 327-338 ◽  
Author(s):  
J.A. Fernández ◽  
T. Gallardo
Keyword(s):  
Total Population ◽  
Complex Function ◽  
Dynamical Evolution ◽  
Oort Cloud ◽  
Capture Process ◽  
Influx Rate ◽  
Short Period ◽  
Dynamical Properties ◽  
Orbital Periods ◽  
Probability Of Capture

AbstractThe Oort cloud probably is the source of Halley-type (HT) comets and perhaps of some Jupiter-family (JF) comets. The process of capture of Oort cloud comets into HT comets by planetary perturbations and its efficiency are very important problems in comet ary dynamics. A small fraction of comets coming from the Oort cloud − of about 10−2− are found to become HT comets (orbital periods < 200 yr). The steady-state population of HT comets is a complex function of the influx rate of new comets, the probability of capture and their physical lifetimes. From the discovery rate of active HT comets, their total population can be estimated to be of a few hundreds for perihelion distancesq <2 AU. Randomly-oriented LP comets captured into short-period orbits (orbital periods < 20 yr) show dynamical properties that do not match the observed properties of JF comets, in particular the distribution of their orbital inclinations, so Oort cloud comets can be ruled out as a suitable source for most JF comets. The scope of this presentation is to review the capture process of new comets into HT and short-period orbits, including the possibility that some of them may become sungrazers during their dynamical evolution.

Exploring Coronal Structures with SOHO

2000 ◽  
Vol 179 ◽  
pp. 403-406
Author(s):  
M. Karovska ◽  
B. Wood ◽  
J. Chen ◽  
J. Cook ◽  
R. Howard
Keyword(s):  
Solar Corona ◽  
Image Enhancement ◽  
Coronal Mass Ejections ◽  
Dynamical Evolution ◽  
Small Scale ◽  
Low Contrast ◽  
Contrast Structures ◽  
Scale Structures ◽  
Small Scale Structures ◽  
Coronal Structures

AbstractWe applied advanced image enhancement techniques to explore in detail the characteristics of the small-scale structures and/or the low contrast structures in several Coronal Mass Ejections (CMEs) observed by SOHO. We highlight here the results from our studies of the morphology and dynamical evolution of CME structures in the solar corona using two instruments on board SOHO: LASCO and EIT.

Evolution of collisional systems

1984 ◽  
Vol 75 ◽  
pp. 361-362
Author(s):  
André Brahic
Keyword(s):  
Gravitational Field ◽  
Dynamical Evolution ◽  
Oblate Planet

AbstractThe dynamical evolution of planetary discs in the gravitational field of an oblate planet and a satellite is numerically simulated.

The Jovian ring

1984 ◽  
Vol 75 ◽  
pp. 203-209
Author(s):  
Joseph A. Burns
Keyword(s):  
Equatorial Plane ◽  
Charged Particles ◽  
Dynamical Evolution ◽  
Main Band ◽  
Small Grains ◽  
Three Components

ABSTRACTLying in Jupiter's equatorial plane is a diaphanous ring having little substructure within its three components (main band, faint disk, and halo). Micron-sized grains account for much of the visible ring, but particles of centimeter sizes and larger must also be present to absorb charged particles. Since dynamical evolution times and survival life times are quite short (≲102-3yr) for small grains, the Jovian ring is being continually replenished; probably most of the visible ring is generated by micrometeoroids colliding into unseen parent bodies that reside in the main band.

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