Rogue Waves Research Articles

Study of Optical Rogue Waves in Two-Dimensional Disordered Lattices

We probed the impact of both the degree of disorder and nonlinearity on rogue waves (RWs) in two-dimensional disordered lattices. Our results unveiled that an increase in the disorder level under linear conditions heightened the probability of RW occurrence and simultaneously contracted the “long tail”. Interestingly, with the introduction of nonlinearity, this “long tail” became shorter compared with linear conditions. Nevertheless, in the context of disordered media, RW occurrence probability demonstrated relative stability—a distinct deviation from its conduct within homogeneous media.

Surface engineering by rogue wave induced by energetic carbon clusters

Abstract Swift heavy ions are effective in nanostructuring of materials surfaces. The irradiation of lanthanum fluoride with 30 MeV C60 leads to the creation of surface nanohillocks of size larger than the ones produced by monoatomic heavy ions. The generation of the observed nano-sized hillocks are described here by a new approach, which is based on ion-induced intensive electronic excitations that create localised rogue waves. Consequently, the induced nonlinear ion-acoustic rogue waves are considered as a hallmark of nanohillocks formation. Plasma hydrodynamic equations produce a relationship between normalised electron number density and crystal lattice spacing. Similarities to the hillock profile suggest the crucial primary role of electron density in the fabrication of surface nanostructures.

The Expected Dynamics for the Extreme Wind and Wave Conditions at the Mouths of the Danube River in Connection with the Navigation Hazards

The entrance in the Sulina channel in the Black Sea is the target area of this study. This represents the southern gate of the seventh Pan-European transport corridor, and it is usually subjected to high navigation traffic. The main objective of the work is to provide a more comprehensive picture concerning the past and future expected dynamics of the environmental matrix in this coastal area, including especially the extreme wind and wave conditions in connection with the possible navigation risks. The methodology considered assumes analyses performed at three different levels. First, an analysis of some in situ measurements at the zero-kilometer point of the Danube is carried out for the 15-year period of 2009–2023. Together with the maximum wind speed and the maximum value of the wind gusts, the water level variation was analyzed at this point. As a second step, the analysis is based on wind speed data provided by regional climate models. Two periods, each spanning 30 years, are considered. These are the recent past (1976–2005), when comparisons with ERA5 reanalysis data were also performed, and the near future (2041–2070), when two different models and three climate scenarios were considered. The focus was on the extreme wind speed values, performing comparisons between the past and future expected extreme winds. Finally, the third analysis is related to the wave conditions. Thus, using as a forcing factor each of the wind fields that was previously analyzed, simulations employing a spectral wave model were carried out. The wave modeling system was focused using three different computational domains with increasing resolution towards the target area, and the nearshore wave conditions were evaluated. The results show that both the extreme wind and wave conditions are expected to slightly increase in the future. Especially in the wintertime, strong wind fields are often expected in this area, with wind gusts exceeding more than 70% of the hourly average wind velocity. With regard to the waves, due to the complex nearshore phenomena, considerable enhancements in terms of significant wave heights are induced, and there is also an elevated risk of the occurrence of rogue waves. This work is still ongoing, and taking into account the high navigation risks highlighted, the next step would be to elaborate the risk assessment of severe shipping conditions, particularly related to the likelihood or probability of adverse conditions with the potential of generating hazardous situations in this coastal environment.

Association of minor electrocardiographic (ECG) abnormalities with epilepsy duration in children: A manifestation of the epileptic heart?

PurposeCardiac abnormalities resulting from chronic epilepsy (“the epileptic heart”) constitute a well-recognized comorbidity. However, the association of cardiac alterations with epilepsy duration remains understudied. We sought to evaluate this association using electrocardiogram (ECG). MethodsWe prospectively enrolled children between 1 months and 18 years of age without known cardiac conditions or ion channelopathies during routine clinic visits. ECGs were categorized as abnormal if there were alterations in rhythm; PR, QRS, or corrected QT interval; QRS axis or morphology; ST segment or T wave. An independent association between ECG abnormalities and epilepsy duration was evaluated using multivariable logistic regression modeling. Results213 children were enrolled. 100 ECGs (47%) exhibited at least one alteration; most commonly in the ST segment (37, 17%) and T wave (29, 11%). Children with normal ECGs had shorter epilepsy duration as compared to those with ECG abnormalities (46 [18–91] months vs. 73 [32–128 months], p = 0.004). A multivariable logistic regression model demonstrated that increasing epilepsy duration was independently associated with the presence of ECG abnormalities (OR=1.09, 95% CI=1.02–1.16, p = 0.008), adjusted for seizure frequency, generalized tonic-clonic/focal to bilateral tonic-clonic seizures as the predominant seizure type, and number of channel-modifying anti-seizure medications. Increasing epilepsy duration was also independently associated with the presence of ST/T wave abnormalities (OR=1.09, 95% CI=1.01–1.16, p = 0.017), adjusted for the same covariates. SignificanceIncreasing epilepsy duration is independently associated with the presence of minor ECG abnormalities. Additional studies are needed to evaluate whether this finding may represent a manifestation of the “epileptic heart”.

Study of lump and periodic waves along with rogue waves and breathers for mathematical modeling of biological dynamical system

Globally, infectious diseases pose a significant threat. Notable cases include influenza, Hepatitis B and HIV. COVID-19, caused by the coronavirus, has been the subject of recent discussion due to its great transmissibility. This study explores the Susceptible–Infectious–Recovered (SIR) epidemic model, explaining several analytical approaches to comprehend the nonlinear incident rates and geographic dispersion. The model investigates phenomena such as M-shaped solitons, homoclinic breather-like solitons, lump waves (LWs), lump solution (LS) with one or two kinks, rogue waves (RWs), periodic waves (PWs) and periodic cross-kink waves. These solutions aid in understanding the disease spread and informing containment strategies by identifying optimal outbreak control methods. This work studies localized wave solutions in nonlinear wave equations, known as soliton solutions including the LS. RWs are characterized by unexpectedly large amplitude and rapid profile changes, drawing attention for their erratic features. PWs exhibit periodic repetitions over time and space. Besides, some type of solitons with special waveforms are the periodic cross-kink, M-shaped and homoclinic breather-like solitons. Graphical representation visualizes the behavior of these effective waves, providing insights into virus spread in specific regions over time. SIR models help identify optimal strategies for controlling outbreaks. The work adds to our understanding of epidemic dynamics by illuminating how the movement of susceptible and infected individuals affects the spread of disease.

Soliton molecules, breather molecules and stability analysis of the three-coupled nonlinear Schrodinger equation

Abstract We investigate the three-coupled nonlinear Schrodinger (NLS) equation, which holds a significant physical implications in optical communications and biophysics. The multi-soliton solutions are derived utilizing the Hirota bilinear method. Multi-breather solutions are presented by assuming certain relationship for the parameters of the multi-solitons. By introducing the velocity resonance mechanism to multiple soliton/breather solutions, it is found that the three-coupled NLS model possesses abundant soliton molecule, breather molecule and breather-soliton molecule structures. The interactions among different types of soliton molecules which can be observed in marine and oceanic waters are investigated through numerical simulation. Ultimately, baseband modulation instability of the three-coupled NLS equation is analyzed. It is highly significance for the study of soliton formation and rogue waves in the three-coupled NLS equation.

Synthetic Fentanyl and Xylazine—The New Rogue Wave of the Opioid Crisis: A Neuroimaging Case Series of “Tranq-Dope” Overdoses (P6-2.003)

Synthetic Fentanyl and Xylazine—The New Rogue Wave of the Opioid Crisis: A Neuroimaging Case Series of “Tranq-Dope” Overdoses (P6-2.003)

High-Energy Pacing Inhibits Slow Wave Dysrhythmias in the Small Intestine.

The motility of the gastrointestinal tract is coordinated in part by rhythmic slow waves, and disrupted slow wave patterns are linked to functional motility disorders. At present, there are no treatment strategies that primarily target slow wave activity. This study assessed the use of pacing to suppress glucagon-induced slow wave dysrhythmias in the small intestine. Slow waves in the jejunum were mapped in vivo using a high-resolution surface-contact electrode array in pigs (n=7). Glucagon was intravenously administered to induce hyperglycemia. Slow wave propagation patterns were categorized into antegrade, retrograde, collision, pacemaker and uncoupled activity. Slow wave characteristics such as period, amplitude and speed were also quantified. Post-glucagon infusion, pacing was applied at 4 mA and 8 mA and the resulting slow waves were quantified spatiotemporally. Antegrade propagation was dominant throughout all stages with a prevalence of 55 ± 38% at baseline. However, glucagon infusion resulted in a substantial and significant increase in uncoupled slow waves from 10 ± 8% to 30 ± 12% (p=0.004) without significantly altering the prevalence of other slow wave patterns. Slow wave frequency, amplitude and speed remained unchanged. Pacing, particularly at 8 mA, significantly suppressed dysrhythmic slow wave patterns and achieved more effective spatial entrainment (85%) compared to 4 mA (46%, p=0.039).This study defined the effect of glucagon on jejunal slow waves and identified uncoupling as a key dysrhythmia signature. Pacing effectively entrained rhythmic activity and suppressed dysrhythmias, highlighting the potential of pacing for gastrointestinal disorders associated with slow wave abnormalities.

Quantitative analysis of the intensity distribution of optical rogue waves

The field of optical rogue waves is a rapidly expanding topic with a focus on explaining their emergence. To complement this research, instead of providing a microscopic model that generates extreme events, we concentrate on a general quantitative description of the observed behavior. We explore two complementary top-down approaches to estimating the exponent describing the power-law decaying distribution of optical rogue waves observed in supercontinuum generated in a single-mode fiber in the normal-dispersion regime by applying a highly fluctuating pump. The two distinct approaches provide consistent results, outperforming the standard Hill estimator. Further analysis of the distributions reveals the breakdown of power-law behavior due to pump depletion and detector saturation. Either of our methods is adaptable to analyze extreme-intensity events from arbitrary experimental data.

Localized wave solutions to coupled variable-coefficient fourth-order nonlinear Schrödinger equations

This study investigates higher-order localized waves for coupled variable-coefficient fourth-order nonlinear Schrödinger equations, which are used to describe the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the seed solutions and Lax pair, the Nth-order localized wave solutions are constructed. The interactions of rogue waves with dark–bright solitons are graphically analyzed via numerical simulation. The results are helpful for studying localized wave phenomena in nonlinear optics.

Dynamical analysis of optical soliton solutions for CGL equation with Kerr law nonlinearity in classical, truncated [formula omitted]-fractional derivative, beta fractional derivative, and conformable fractional derivative types

The study of optical soliton solutions plays a vital role in nonlinear optics. The foremost area of optical solitons research encompasses around optical fiber, telecommunication, meta-surfaces and others related technologies. The aim of this work is to integrate optical soliton solutions of the complex Ginzburg-Landau (CGL) model with Kerr law nonlinearity, also showing the effect of diverse fraction derivative and comparing it with the classical form. Here, the local derivative is used as the conformable wisdom known as the truncated M-fractional derivative, beta fractional derivative, and conformable fraction derivative. We also deliberated on some assets satisfied by the derivative. The CGL model is useful to describe the light propagation in optical communications, optical transmission, and nonlinear optical fiber. Under the right circumstances, the affectionate unified scheme is implemented for the complex Ginzburg-Landau model to generate the optical wave pattern. For α1=2α2, the unified scheme generates the solution of CGL model in terms of hyperbolic, trigonometric, and rational function solutions. This scheme provides some novel optical solitons such as periodic waves, periodic with rogue waves, breather waves, different types of periodic rogue waves, a singular soliton solution, and rogue with the periodic wave for the special value of the free parameters. For α2=-ρ+6α18, the unified scheme generates the solutions of CGL model in terms of hyperbolic, trigonometric, and rational function solutions. This scheme offers some fresh optical solitons such as periodic rogue waves, multi-rogue waves, double periodic waves, and periodic waves. In numerical argument, the wave patterns are offered with 3-D and density plots. To test the stability of the obtained solutions, we show diverse fractional forms such as beta time fractional, and conformable time fractional derivative and compare these fractional derivatives with their classical form in 2D plots. The investigation reveals innovative and explicit solutions, providing insight into the dynamics of the related physical processes. This paper provides a comprehensive examination of the obtained solutions, emphasizing their distinct features and depictions using unified technique. These findings are especially advantageous for specialists in the fields of nonlinear science and mathematical physics, providing significant insights into the behavior and development of nonlinear waves in various physical situations.

Breathers for the sixth-order nonlinear Schrödinger equation on the plane wave and periodic wave background

In this paper, we study the breathers in the framework of the sixth-order nonlinear Schrödinger equation by using the Darboux transformation. The primary objective of this research is twofold. First, we consider the nonlinear superposition of breathers on the plane wave background. Based on the concept that rogue waves are formed from colliding Akhmediev breathers, we obtain rogue wave sequences and a first-order Akhmediev breather with a central second-order rogue wave peak. Second, we consider the formation of breathers on the periodic wave background. The difficulty of solving the Lax pair is overcome, and we successfully construct the breathers on the cn- and dn-periodic wave background.

Rogue wave pattern of multi-component derivative nonlinear Schrödinger equations.

This paper studies the multi-component derivative nonlinear Schrödinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation method, we derive higher-order vector rogue wave solutions for the n-DNLS equations. Specifically, we focus on the distinctive scenario where the (n+1)-order characteristic polynomial possesses an explicit (n+1)-multiple root. Additionally, we provide an in-depth analysis of the asymptotic dynamic behaviors and pattern classification inherent to the higher-order vector rogue wave solution of the n-DNLS equations, mainly when one of the internal arbitrary parameters is extremely large. These patterns are related to the root structures in the generalized Wronskian-Hermite polynomial hierarchies.

Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations

A solitary wave, characterized as a localized perturbation in a medium, emerges as a result of a delicate equilibrium between nonlinear and dispersive phenomena. Solitons, a subtype of solitary waves, exhibit persistent shape and velocity during propagation, representing a fundamental phenomenon observed widely in natural systems and possessing various applications in nonlinear dynamics. This investigation focuses on two nonlinear evolution equations (NEEs), specifically the Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation and the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony (GZKBBM) equation, which find relevance in domains such as fluid dynamics and ocean engineering. Utilizing an ansatz-based methodology, soliton solutions of both bright and dark characteristics are derived, alongside exploration of rogue wave-type solutions. Notably, the manifestation of dark, bright, and rogue waves aligns with the physical interpretation of the generated solitons. Computational simulations conducted using Wolfram Mathematica aim to provide a comprehensive description of the physical phenomena. The novelty of this study lies in its unreported investigation, contributing new insights into the solitonic dynamics within the considered models.

PT-symmetric PINN for integrable nonlocal equations: Forward and inverse problems.

Since the PT-symmetric nonlocal equations contain the physical information of the PT-symmetric, it is very appropriate to embed the physical information of the PT-symmetric into the loss function of PINN, named PTS-PINN. For general PT-symmetric nonlocal equations, especially those equations involving the derivation of nonlocal terms due to the existence of nonlocal terms, directly using the original PINN method to solve such nonlocal equations will face certain challenges. This problem can be solved by the PTS-PINN method, which can be illustrated in two aspects. First, we treat the nonlocal term of the equation as a new local component so that the equation is coupled at this time. In this way, we successfully avoid differentiating nonlocal terms in neural networks. On the other hand, in order to improve the accuracy, we make a second improvement, which is to embed the physical information of the PT-symmetric into the loss function. Through a series of independent numerical experiments, we evaluate the efficacy of PTS-PINN in tackling the forward and inverse problems for the nonlocal NLS equation, the nonlocal derivative NLS equation, the nonlocal (2+1)-dimensional NLS equation, and the nonlocal three-wave interaction systems. The numerical experiments demonstrate that PTS-PINN has good performance. In particular, PTS-PINN has also demonstrated an extraordinary ability to learn large space-time scale rogue waves for nonlocal equations.

Tolerance of Tourists in Praying in the Prayer Well Room of the Aceh Tsunami Museum

Indonesia is a maritime country located between three world plates that move together, so Indonesia is a country that has a high earthquake rate. Earthquakes that occur at sea can cause giant waves (tsunami). One of the tsunamis that occurred in Indonesia was the Aceh tsunami in 2004. To commemorate this incident, the Aceh Tsunami Museum was built. This museum was built on December 26 2009, so that the victims of the Tsunami disaster would not be forgotten, then as a safety education center, and an evacuation center if another Tsunami occurred. Inside the Tsunami Museum there is a room called the wishing well. On the walls of the prayer well room are the names of the victims of the Aceh Tsunami. Every visitor who enters here is encouraged to pray for the victims according to their respective beliefs. This is where we can see religious tolerance. The formulation of the research problem is how is the tolerance of tourists in praying in the space of sorrow (praying well room) of the Aceh Tsunami Museum? This research aims to determine the tolerance of tourists in praying in the space of sorrow (praying well room) of the Aceh tsunami museum. The method in this research is a qualitative approach where interviews and observations are carried out. The results obtained from the field will be analyzed and described in detail by researchers. The results of this research are that every visitor has a high level of tolerance

Rogue waves for the (2+1)-dimensional Myrzakulov–Lakshmanan-IV equation on a periodic background

In this paper, the rogue wave solutions of the (2+1)-dimensional Myrzakulov–Lakshmanan (ML)-IV equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation (DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are obtained. The relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.

Mixed localized waves in the coupled nonlinear Schrödinger equation with higher-order effects

In this work, the coupled nonlinear Schrödinger equation with higher-order effects is studied with the aid of Darboux transformation and an asymptotic analysis. We report mixed localized waves, rogue wave coexisting with breathers in the system. Under certain constraints, the structures and evolutionary processes of solutions have been influenced. For example, The phase, amplitude, and propagating direction of mixed localized waves change when rogue wave collides with breathers. Moreover, the localized waves characteristics together with collision dynamic behaviors of these explicit rogue wave and breathers are exhibited graphically and discussed in detail. These novel results may be meaningful to study integrable systems better.

Active Tunable Elastic Metasurface for Abnormal Flexural Wave Transmission

An active elastic metasurface has more flexibility than a passively modulated elastic metasurface, owing to the manipulation of the phase gradient that can be realized without changing the geometrical configuration. In this study, a negative proportional feedback control system was employed to provide positive active control stiffness for adaptive unit cells, with the aim of achieving the active modulation of the phase gradient. The relationship between the control gain and the phase velocity of the flexural wave was derived, and the transfer coefficients and phase shifts of the flexural wave through the adaptive unit cells were resolved using the transfer matrix method. Finite element simulations for wave propagations in the adaptive unit cells were conducted, and they verified the analytic solutions. Based on this theoretical and numerical work, we designed active elastic metasurfaces with adaptive unit cells with sub-wavelength thicknesses according to the generalized Snell’s law. These metasurfaces show flexibility in achieving abnormal functions for transmitted waves, including negative refraction and wave focusing, and transforming guided waves at different operating frequencies by manipulating the control gain. Therefore, the proposed active metasurface has great potential in the fields of the tunable manipulation of elastic waves and the design of smart devices.

Interaction solutions of (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation via bilinear method

Using the bilinear neural network method (BNNM) and the symbolic computation system Mathematica, this paper explains how to find an exact solution for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani (KdVSKR) equation. In terms of activation function and weight coefficient, BNNM is a more appealing option for users than traditional symbolic computation methods. It is possible to develop a wide range of solutions and expand the classes of exact solutions by modifying the activation function. The activation function’s versatility allows it to generate a wide range of solutions with several theoretical and practical uses. The analytical solution is obtained by using a double layer type, while the rogue wave solution and mixed solutions are obtained by using a single layer type. The evolution of these waves is then illustrated using various 3D graphs, 2D graphs, and density plots.