Article
Physics, Multidisciplinary
Noufe H. Aljahdaly, S. A. El-Tantawy, H. A. Ashi, Abdul-Majid Wazwaz
Summary: The study employs numerical methods to investigate dissipative freak waves and breathers in collisional electronegative complex plasmas, reducing the fluid equation of plasma species to the linear damped nonlinear Schrodinger equation. By studying modulational instability and the effect of plasma parameters on the behavior of dissipative structures, the impact of plasma configuration parameters on the (un)stable envelope structures is discussed, while examining the profiles of dissipative waves and breathers in relation to plasma configuration parameters.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Engineering, Mechanical
Sarah Alwashahi, Najdan B. Aleksic, Milivoj R. Belic, Stanko N. Nikolic
Summary: In this work, the authors investigate different shapes of rogue wave clusters composed of Kuznetsov-Ma solitons from the nonlinear Schrodinger equation with Kerr nonlinearity. They present three classes of higher-order solutions obtained using the Darboux transformation scheme. The work demonstrates the incredible power of the scheme in creating new solutions and the richness in form and function of those solutions.
NONLINEAR DYNAMICS
(2023)
Article
Multidisciplinary Sciences
Miguel Onorato, Luigi Cavaleri, Stephane Randoux, Pierre Suret, Maria Isabel Ruiz, Marta de Alfonso, Alvise Benetazzo
Summary: An impressive and unique wave packet was measured in the Bay of Biscay in the North-East of the Atlantic Ocean, with a spatial extension of over 1 km and the tallest wave reaching 27.8 m, characterized by a non trivial nonlinear content.
SCIENTIFIC REPORTS
(2021)
Article
Mathematics, Applied
Hai-Qiang Zhang, Fa Chen
Summary: This paper investigates rogue wave solutions on a periodic background for the fourth-order nonlinear Schrodinger equation, finding them to be modulationally unstable with respect to long-wave perturbations. By combining nonlinearization of spectral problems with the Darboux transformation method, rogue wave solutions on the background of periodic waves are derived. The dynamics of rogue waves are studied, revealing analogs in the standard NLS equation and unaffected magnification factor by higher-order effects. Additionally, the rogue wave solutions can simplify into multi-pole soliton solutions as the elliptic modulus approaches 1, forming weakly bound states.
Article
Mathematics, Applied
Bo Yang, Jianke Yang
Summary: We report new rogue wave patterns in the nonlinear Schrodinger equation that are formed by individual Peregrine waves. These patterns are described asymptotically by root structures of Adler-Moser polynomials and are much more diverse than previous rogue patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy. The analytical predictions of these patterns show good agreement with true solutions.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Engineering, Mechanical
Hai-Qiang Zhang, Rui Liu, Fa Chen
Summary: In this paper, we investigate the behavior of rogue waves on a double-periodic background in a nonlinear Schrodinger equation with higher-order effects. We derive analytical solutions for both double-periodic waves and rogue waves and explore how the higher-order effects affect these waves. The obtained results are significant for understanding the manifestations of rogue waves on double-periodic backgrounds in hydrodynamics and nonlinear optics with higher-order effects.
NONLINEAR DYNAMICS
(2023)
Article
Mechanics
Bachirou Bachir Mouhammadoul, A. Alim, C. G. L. Tiofack, A. Mohamadou, Albandari W. Alrowaily, Sherif. M. E. Ismaeel, S. A. El-Tantawy
Summary: This investigation explores the modulation of weakly positron-acoustic waves (PAWs) in four-component magnetoplasmas with nonextensive electrons and fluid positrons. The researchers derived the nonlinear Schrodinger equation (NLSE) for the PAWs using the derivative expansion technique. Through linear stability analysis, the modulational instability (MI) in the current magnetoplasma model was studied, and it was found that the magnetic field parameter significantly affects the bandwidth and maximum amplitude of the MI. The obtained results have implications for understanding the acceleration mechanism of static electrostatic wave packets in various plasma environments.
Article
Engineering, Mechanical
Stanko N. Nikolic, Sarah Alwashahi, Omar A. Ashour, Siu A. Chin, Najdan B. Aleksic, Milivoj R. Belic
Summary: In this paper, the multi-elliptic rogue wave clusters of the nonlinear Schrodinger equation are analyzed to understand the origin and appearance of optical rogue waves in this system. The Darboux transformation scheme is used to obtain these structures on uniform backgrounds. The main outcomes of this research are the new multi-rogue wave solutions of the NLSE and its extended family.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Omar A. Ashour, Siu A. Chin, Stanko N. Nikolic, Milivoj R. Belic
Summary: We investigated higher-order breathers of the cubic nonlinear Schrodinger equation on a periodic elliptic background. We found that, beyond first order, any arbitrarily constructed breather on a disordered background generates a single-peaked solitary wave. However, on the periodic backgrounds, the so-called quasi-rogue waves, which are quasiperiodic breathers with distorted side peaks, are more common. We constructed such higher-order breathers using constituent first-order breathers with commensurate periods and also found truly periodic breathers, but they are rare and require finely tuned parameters.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Jiguang Rao, Dumitru Mihalache, Jingsong He, Yi Cheng
Summary: This paper reports three families of general higher-order rogue wave solutions to the two-component nonlinear Schrodinger equation coupled to the Boussinesq equation. The properties and boundedness of these solutions are described.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mechanics
Junpeng Liu, Xingya Feng, Junnan Cui
Summary: The PB solution of the nonlinear Schrodinger equation is used to model ocean extreme waves, showing triangular spectral features over the nonlinear evolution. A background random wave is superposed to the PB to simulate a more realistic sea state. Spectral analysis reveals that the wave elevations exhibit similar triangular spectral features with a relatively mild background wave. Furthermore, the second harmonic elevations of the extreme waves also exhibit triangular spectral features, suggesting the potential use of both first and second harmonic elevations for the detection of extreme wave formation.
Article
Engineering, Mechanical
Milivoj R. Belic, Stanko N. Nikolic, Omar A. Ashour, Najdan B. Aleksic
Summary: This article discusses the strange nature, dynamic generation, ingrained instability, and potential applications of rogue waves in oceans and optics. It presents solutions to the standard cubic nonlinear Schrodinger equation, which models many propagation phenomena in nonlinear optics. The article proposes a method for suppressing the modulation instability of rogue waves and demonstrates how rogue waves can be used to produce stable recurrent images in nanolithography. It also highlights instances when rogue waves appear as numerical artifacts and how statistical analysis based on different numerical procedures can lead to misleading conclusions about the nature of rogue waves.
NONLINEAR DYNAMICS
(2022)
Article
Mechanics
Alexey Slunyaev
Summary: In the direct numerical simulation of deep water nonlinear unidirectional irregular waves, a wave group lasting for more than 200 periods was identified as an intense envelope soliton with remarkably stable parameters. Most extreme waves occur on top of this group, resulting in higher and longer rogue wave events.
Article
Mathematics, Interdisciplinary Applications
Jingxuan Geng, Huanhe Dong, Jing Xu, Lei Fu
Summary: In this paper, the third-order coupled nonlinear Schrodinger equations are derived from the original equations for two-layer plane, which describe the evolution of two internal gravity waves in the mesoscale atmosphere. Vector rogue wave solutions, which are mechanisms for rainstorm formation, can be obtained through integral preserving transformations. Modulation instability (MI) analysis reveals that the existence of rogue waves is determined by a special MI, namely baseband MI. This may provide a theoretical basis for predicting vector rogue waves.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Li Wang, Zhenya Yan
Summary: This paper investigates novel nonlinear wave structures in the defocusing nonlinear Schrodinger equation, including stable new rogue waves (RW) and W-shaped solitons, as well as the interactions of RWs and the presence of RWs and W-shaped solitons in the case of complex PT-symmetric potentials.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mechanics
Gennady A. El
Summary: This study reviews the spectral theory of soliton gases in integrable dispersive hydrodynamic systems by presenting both a phenomenological approach based on phase shifts in pairwise soliton collisions and a more detailed theory modeling soliton gas dynamics by a thermodynamic limit of modulated finite-gap spectral solutions of the Korteweg-de Vries and focusing NLS equations. The integrability properties of the kinetic equation for soliton gas are discussed, and physically relevant solutions are compared with direct numerical simulations of dispersive hydrodynamic systems.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Editorial Material
Physics, Multidisciplinary
Pierre Suret
Article
Physics, Fluids & Plasmas
Alexey Tikan, Felicien Bonnefoy, Giacomo Roberti, Gennady El, Alexander Tovbis, Guillaume Ducrozet, Annette Cazaubiel, Gaurav Prabhudesai, Guillaume Michel, Francois Copie, Eric Falcon, Stephane Randoux, Pierre Suret
Summary: The Peregrine soliton (PS) is a prototype nonlinear structure that captures the properties of rogue waves. Recent research has shown that the PS can emerge independently of its solitonic content from partially radiative or solitonless initial data. In this study, the researchers controlled the occurrence of the PS in space-time by adjusting the initial chirp. The proposed method of nonlinear spectral engineering was found to be robust to higher-order nonlinear effects.
PHYSICAL REVIEW FLUIDS
(2022)
Article
Optics
Francois Copie, Pierre Suret, Stephane Randoux
Summary: In this study, we experimentally investigate higher-order seeded modulation instability in an optical fiber experiment. By using a recirculating loop configuration with round trip losses compensation, we are able to observe, in a single-shot, the spatiotemporal evolution of an initially modulated continuous field, revealing intricate yet deterministic dynamics. We observe a continuous transition between perfectly coherent and purely noise-driven dynamics by tuning the modulation period, which we characterize by means of a statistical study.
Article
Physics, Multidisciplinary
Thibault Bonnemain, Benjamin Doyon, Gennady El
Summary: We establish the correspondence between soliton gases in classical integrable dispersive hydrodynamics and generalized hydrodynamics (GHD), and predict various physical quantities for the soliton gas by constructing the GHD description for the Korteweg-de Vries equation. We validate these predictions by numerical simulations and propose conjectured dynamical correlation functions for the soliton gas based on GHD results.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Albert F. Adiyatullin, Lavi K. Upreti, Corentin Lechevalier, Clement Evain, Francois Copie, Pierre Suret, Stephane Randoux, Pierre Delplace, Alberto Amo
Summary: By implementing a synthetic photonic lattice in a two-coupled ring system, we have successfully designed an anomalous Floquet metal that exhibits two different topological properties in its gapless bulk. Firstly, this synthetic lattice features bands characterized by a winding number, which emerges from the breakup of inversion symmetry and is directly linked to the appearance of Bloch suboscillations in its bulk. Secondly, the Floquet nature of the lattice leads to well-known anomalous insulating phases with topological edge states. The combination of broken inversion symmetry and periodic time modulation studied here enriches the range of topological phases available in lattices subject to Floquet driving, and suggests the potential emergence of novel phases when periodic modulation is combined with the breakup of spatial symmetries.
PHYSICAL REVIEW LETTERS
(2023)
Article
Mathematics, Applied
T. Congy, G. A. El, G. Roberti, A. Tovbis
Summary: In this paper, we study the large-scale dynamics of a non-equilibrium dense soliton gas described by the Korteweg-de Vries (KdV) equation. We prove that in the special condensate limit, the integro-differential kinetic equation for the spectral density of states reduces to the N-phase KdV-Whitham modulation equations. By analyzing the Riemann problems and solving the kinetic equation, we obtain explicit solutions for generalized rarefaction and dispersive shock waves. Numerical results for diluted soliton condensates exhibiting incoherent behaviors associated with integrable turbulence are also presented.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Optics
A. Villois, D. N. Puzyrev, D. Skryabin, M. Onorato
Summary: Dissipative solitons in optical microcavities have been a subject of great interest due to their connection with the generation of optical frequency combs. In this study, we investigate dissipative soliton breathers in a microresonator with second-order nonlinearity, specifically at the exact phase matching for efficient second-harmonic generation. We emphasize the significant role of the group-velocity difference between the first- and second-harmonic pulses for the existence of breathers. Additionally, we observe the phenomenon of dissipative-breather-gas, where multiple breathers propagate randomly in the resonator and collide elastically.
Article
Optics
Umberto Giuriato, Giorgio Krstulovic, Miguel Onorato, Davide Proment
Summary: Stokes drift is a classical fluid effect where momentum is transferred from traveling waves to tracers of the fluid, resulting in a nonzero drift velocity in the direction of the waves. This phenomenon allows particles (impurities) to be transported by the flow. In quantum fluids, impurities are driven by inertial effects and pressure gradients, and our theoretical predictions show that the drift direction and amplitude depend on the initial impurity position and the relative particle-fluid density ratio.
Article
Mathematics, Applied
Dmitry Agafontsev, Andrey Gelash, Stephane Randoux, Pierre Suret
Summary: This paper presents a universal method for constructing localized solutions from exact multisoliton solutions, which can simulate the localized characteristics of rogue waves. The method replaces the plane wave in the dressing construction of breathers with a specific exact N-soliton solution, which converges asymptotically to the plane wave. The constructed multisoliton solutions, with their characteristic width proportional to N, are practically indistinguishable from breathers in a wide region of space and time at large N.
STUDIES IN APPLIED MATHEMATICS
(2023)
Article
Physics, Fluids & Plasmas
Francesco De Vita, Giovanni Dematteis, Raffaele Mazzilli, Davide Proment, Yuri V. Lvov, Miguel Onorato
Summary: One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids, and the wave kinetic equation is used to study thermal conduction. The study reveals the interaction between high and low wave numbers in thermal conduction.
Article
Physics, Fluids & Plasmas
M. Onorato, G. Dematteis, D. Proment, A. Pezzi, M. Ballarin, L. Rondoni
Summary: In this study, we predict the presence of negative temperature states in the discrete nonlinear Schodinger (DNLS) equation and provide exact solutions using the associated wave kinetic equation. We define an entropy within the wave kinetic approach that monotonically increases in time and reaches a stationary state in accordance with classical equilibrium statistical mechanics. Our analysis shows that fluctuations of actions at fixed wave numbers relax to their equilibrium behavior faster than the spectrum reaches equilibrium. Numerical simulations of the DNLS equation confirm our theoretical results. The boundedness of the dispersion relation is found to be critical for observing negative temperatures in lattices characterized by two invariants.
Article
Physics, Multidisciplinary
Tinggui Chen, Baizhan Xia, Dejie Yu, Chuanxing Bi
Summary: This study proposes a gradient phononic crystal structure for enhanced acoustic sensing. By breaking the symmetry of the PC structure, topologically protected edge states are introduced, resulting in topological acoustic rainbow trapping. The robustness and enhancement properties are verified numerically and experimentally.
