Rogue Wave Profiles Research Articles

Evolution of nanohillocks by fullerene ion-induced localized plasma

Surface nanostructures etch without chemicals; owing to this, their development is a crucial technical process. Surface nanohillocks may be created by irradiating yttrium iron garnet (YIG) with 30-MeV C60 cluster ions. The nanohillock creation mechanism is disputed. In this study, we propose that the formation mechanism is a plasma collective effect of charged particles that depends on localized rogue waves. Rogue waves will explain YIG surface nanohillock creation using a traditional hydrodynamic plasma model. Analytically solving hydrodynamic ion fluid equations and Maxwellian electron distributions yields a non-linear Schrödinger equation. Solving the latter gives us plausible rogue wave domains. Rogue waves concentrate charged ions from the surroundings into a small, confined zone, generating surface nanohillocks. The relevance of different plasma parameters is highlighted in the rogue wave profile.

SIMULATION OF WAVE SOLUTIONS OF A FRACTIONAL-ORDER BIOLOGICAL POPULATION MODEL

In this analysis, we apply prominent mathematical systems like the modified (G’/G)-expansion method and the variation of (G’/G)-expansion method to the nonlinear fractional-order biological population model. We formulate twenty-three mathematical solutions, which are clarified hyperbolic, trigonometric, and rational. Using MATLAB software, we illustrate two-dimensional, three-dimensional, and contour shapes of our obtained solutions. These mathematical systems depict and display its considerate and understandable technique that generates a king type shape, singular king shapes, soliton solutions, singular lump and multiple lump shapes, periodic lump and rouge, the intersection of king and lump wave profile, and the intersection of lump and rogue wave profile. Measuring our return and that gained in the past released research shows the novelty of our analysis. These systems are also capable to represents various solutions for other fractional models in the field of applied mathematics, physics, and engineering.

Dust-ion acoustic rogue waves in six-component dusty plasma

In this work, we investigate the modulational instability of finite amplitude dust-ion acoustic nonlinear waves in a six-component cometary dusty plasma. Such plasma system is composed of Oxygen ion-pair, negative dust particles, kappa distributed light ions of Hydrogen, solar electrons and cometary electrons of the comet tail. By employing the standard reductive perturbation technique, a nonlinear Schrödinger-type equation is obtained. This equation governs the investigation of the modulational instability of finite amplitude dust-ion acoustic nonlinear waves. Our analysis shows two parametric domains, where the dust-ion acoustic waves are modulationally stable and unstable depending on the plasma configurational parameters. Within the unstable domain, rogue waves could be generated due to the nonlinear and dispersion properties of plasma system. The effects of some relevant plasma parameters on the profile of rogue waves are studied. The obtained results might be useful for better understanding the modulational instability of nonlinear plasma waves and formation of dust-ion acoustic rogue waves in space plasmas.

Nonlinear dust-acoustic modes in homogeneous dusty plasmas: bifurcation analysis

Different nonlinear dynamical behavior of dust-acoustic modes of a homogeneous plasma are examined. The plasma composed of negatively charged dust grains and nonextensive distribution electrons and ions. The evolution of the system is investigated using a 3-dimensional nonlinear Schrodinger (3D-NLS) equation. Different methods are used to explore the possible solutions of 3D-NLS equation using a bifurcation analysis and factorization method to obtain periodic, shocklike and explosive waves. Furthermore, rogue wave solution of the 3D-NLS equation is obtained to investigate the dependence of rogue wave profile on nonextensivity parameters. The present investigation can be relevance to the electrostatic structures in various dusty plasmas, such as Saturn’s E-ring.

Multimode excitation and modulational instability of beam plasma system with Tsallis-distributed electrons

In the present investigation, authors have studied the linear mode structure of electron-acoustic waves, their modulational instability and rogue wave profiles in four-component plasma system consisting of stationary ions, cold electron fluid, Tsallis-distributed hot electrons and an electron beam. By applying standard perturbation method to the fluid equations, the dispersion relation is obtained that depends on various parameters such as beam density, beam velocity, beam temperature and non-extensivity q. Based on the phase velocities, two electron-acoustic (EA) modes known as slow and fast, have been extracted as real modes for which a detailed analysis is presented. Further, the basic set of equations is reduced to nonlinear Schrodinger equation (NLSE), where the nonlinearity and dispersion coefficients compete and significantly affect the stability characteristics of EA waves. For both the modes, a comprehensive study of modulational instability and rogue wave profile has been carried out by taking into consideration the effect of non-extensivity and beam velocity. The obtained results have been compared with other research works. The present investigation may be relevant to the observation from Viking satellite in the day-side auroral zone.

Rogue wave signals in a coupled anharmonic network: effects of the transverse direction

In this paper, we consider the dynamics of modulated waves in a nonlinear two-dimensional discrete electrical lattice made of several well-known anharmonic modified Noguchi lines coupled transversely to one another with a linear inductor. In the linear limit and depending on the chosen frequency domain, we demonstrate that the network behaves either as a right-handed line or as a left-handed line. We also establish that the band pass character of the modified Noguchi line increases the bandwidth of the allowed frequencies for which the system adopts the left-handed behavior. Based on the reductive perturbation method in the semi-discrete approximation, we derive a (2 + 1)-dimensional nonlinear Schrodinger (2D-NLS) equation governing the dynamics of the small amplitude signals in the system. The specific nature of this amplitude equation is examined, and it appears that its hyperbolic or elliptic character strongly depends on the coupling inductor $$L_{2}$$ . Moreover, using a simple transformation, we reduce the obtained equation to a (1 + 1)-dimensional nonlinear Schrodinger equation (1D-NLS). The exact first- and second-order rogue wave’s solutions of this 2D-NLS equation are derived in bandwidth frequencies where the network may exhibit modulational instability. The results of our investigations display number of interesting rogue wave profiles which have not been observed in the scientific literature. Furthermore, we examine the effects of both the coupling linear inductor $$L_{2}$$ and the nonlinear dispersion factor $$\eta$$ on the characteristics of the rogue waves and also on their propagation through the network. It appears that $$L_{2}$$ and $$\eta$$ can be used to squeeze or stretch the shape of the rogue waves signals traveling in the network. These numerical results are in perfect agreement with the analytical predictions.

New solitonic and rogue wave solutions of a Klein–Gordon equation with quadratic nonlinearity

An analytical investigation is performed on soliton, lump wave solution, and rogue waves in the Klein–Gordon with quadratic nonlinearity through the extended tanh approach, which possesses complicated wave propagation arising in the field of nonlinear optics, theory of quantum field and solid state physics. As a result, an advanced form of interacting analytical solutions is achieved with some unrestricted parameters. Different conditions on the existing parameters of these solutions are found after analyzing its dynamic behavior. Based on the conditions, different type of rogue wave, bright bell and dark bell shape nature of the solutions are considered. The dynamics nonlinear wave solutions are showed in 3D plots with specific values of the existing parameters. Moreover, it is shown that nonlinear wave packets are localized in two dimensions with characteristics of rogue wave profiles.

Nonlinear modulation of quantum electron acoustic waves in a Thomas–Fermi plasma with effects of exchange-correlation

The amplitude modulation of electron acoustic waves (EAWs) is investigated in an unmagnetized four-component quantum plasma containing dynamic cold electron fluid, Thomas–Fermi distributed hot electrons and positrons and immobile ions in presence of exchange-correlation potentials. For this purpose, basic set of quantum hydrodynamic equations is reduced to a nonlinear Schrodinger equation (NLSE) adopting a reductive perturbation technique. The regions of the stable and unstable wave packets are obtained precisely in terms of the intrinsic plasma parameters. It is shown that the NLSE leads to the modulational instability (MI) of EAWs, and the formation of EA rogue waves, which are due to the effects of nonlinearity and dispersion in the propagation of EAWs. The effects of relevant plasma parameters on the MI criterion are numerically investigated. It is also found that the modulated EAW packets can propagate in the form of bright envelope solitons as well as dark envelope solitons. Within the modulational instability region, the dependence of first- and second-order EA rogue wave profiles on the system parameters is discussed.

Rogue wave statistics in (2+1) Gaussian seas I: Narrow-banded distribution

Originally discussed in the context of ocean statistics for oil rig platform decks and satellite data, spatiotemporal exceeding probability distributions have recently been thought to explain the failure of second and third-order nonlinear models of distributions at a fixed point in space. To investigate this possibility, we derive a simplified model for the (2+1) exceeding probability distribution of ocean waves based on the Gaussian random field approach, with a particular interest in rogue waves. Using standard statistical tools, we show that (2+1)) Longuet–Higgins’ distribution does not depend on the spatiotemporal scale of the ocean surface, rather on the directional spectrum and the dimensionless wave height. Moreover, we use extreme value theory Gumbel (1958)[24] to find the expected maximum wave height in (2+1) dimensions, showing that Piterbarg’s framework provides a smaller expected maximum than Adler’s approach. Unfortunately, both are known for assigning maximum heights that do not saturate when the surface area is very large. Taking into account the mean rogue wave profile, we derive a new expression for the maximum wave height that provides realistic estimates. Finally, comparing the theory for the exceeding probability and expected maximum dimensionless height with the North Alwyn data set of Stansell (2004)[47] we conclude that both (2+1) versions of Longuet-Higgins (1952, 1980)[31,34] distributions fail to provide an accurate description of both return period and maximum observed wave heights, thus undermining the argument that the error in ocean wave statistics can be cured by extending point statistics to higher-dimensions.

Evolution of Dissipative Low-Frequency Rogue Waves in Superthermal Dusty Plasmas

The evolution of dissipative dust-ion acoustic (DIA) rogue waves is studied in a collisional dusty plasma with superthermal electrons. Multiple-time-scale reduction shows that the nonlinear dynamics of low-frequency waves reduces to a modified nonlinear Schrodinger (mNLS) equation. This equation captures the main features of modulated waves and shows a criterion in determining the maximum time for the occurrence of the modulational instability. It is found that the impact of such an energetic tail of electrons is to narrow the stability region in a dusty plasma with source and sink. Within the instability window, we have shown that the mNLS equation in a weakly dissipative plasma is responsible for the formation of DIA rogue waves. The possible region for the existence of dissipative rogue waves is precisely defined for physical parameters. It is shown that the rogue wave profile is very sensitive to any changes in the electron superthermality and dissipative parameters.

Breather structures in a plasma with warm ions and Cairns electrons

The modulational instability (MI) of ion‐acoustic waves (IAWs) in a two‐component non‐Maxwellian hot plasma with Cairns distributed electrons is investigated. Using the derivative expansion method, a non‐linear Schrödinger equation (NLSE) is obtained. The criterion for MI, which occurs for small values of the carrier wavenumber, is obtained. It is found that non‐thermal parameter α modifies the criteria for MI instability. The analytical solutions of NLSE in the form of various types of freak waves, including the Peregrine soliton, the Akhmediev breather, and the Kuznetsov–Ma breather, are examined. The effects of the non‐thermal parameter as well as ion‐to‐electron temperature ratio on the rogue wave profile are discussed. Our results should be relevant to wave propagation stability. Non‐thermal models may play an increasingly important role in predicting complex plasma behaviour and understanding the underlying physical processes.

Freezing optical rogue waves by Zeno dynamics

We investigate the Zeno dynamics of the optical rogue waves. Considering their usage in modeling rogue wave dynamics, we analyze the Zeno dynamics of the Akhmediev breathers, Peregrine and Akhmediev–Peregrine soliton solutions of the nonlinear Schrödinger equation. We show that frequent measurements of the wave inhibits its movement in the observation domain for each of these solutions. We analyze the spectra of the rogue waves under Zeno dynamics. We also analyze the effect of observation frequency on the rogue wave profile and on the probability of lingering of the wave in the observation domain. Our results can find potential applications in optics including nonlinear phenomena.

On the shape and likelihood of oceanic rogue waves

We consider the observation and analysis of oceanic rogue waves collected within spatio-temporal (ST) records of 3D wave fields. This class of records, allowing a sea surface region to be retrieved, is appropriate for the observation of rogue waves, which come up as a random phenomenon that can occur at any time and location of the sea surface. To verify this aspect, we used three stereo wave imaging systems to gather ST records of the sea surface elevation, which were collected in different sea conditions. The wave with the ST maximum elevation (happening to be larger than the rogue threshold 1.25Hs) was then isolated within each record, along with its temporal profile. The rogue waves show similar profiles, in agreement with the theory of extreme wave groups. We analyze the rogue wave probability of occurrence, also in the context of ST extreme value distributions, and we conclude that rogue waves are more likely than previously reported; the key point is coming across them, in space as well as in time. The dependence of the rogue wave profile and likelihood on the sea state conditions is also investigated. Results may prove useful in predicting extreme wave occurrence probability and strength during oceanic storms.

Head-on collision between two dust acoustic solitary waves and study of rogue waves in multicomponent dusty plasma

In this investigation, the study of head-on collision between two dust acoustic solitary waves (DASWs) and characteristics of rogue waves in a dusty plasma composed of dust fluid, kappa distributed ions, electrons, and positrons has been presented. Two Korteweg-de Vries equations are derived by employing the extended Poincaré–Lighthill–Kuo reductive perturbation method. The analytical phase shifts and trajectories after head-on collision of two DA solitary waves have been studied numerically. It is found that the presence of superthermal ions, electrons, as well as positrons; concentrations of electrons and positrons; and temperature of electrons and dust have an emphatic influence on the phase shifts after the head-on collision of two rarefactive DA solitary waves. The time evolution of two rarefactive DASWs has also been presented. Further, the generation of dust acoustic rogue waves (DARWs) has been studied in the framework of rational solution of nonlinear Schrödinger equation. The dependence of the rogue wave profile on the relevant physical parameters has been discussed in detail. It is emphasized that the real implementation of our present results may be of great importance in different regions of space and astrophysical environments, especially in the interstellar medium and Jupiter rings.

Ion acoustic kinetic Alfvén rogue waves in two temperature electrons superthermal plasmas

The propagation properties of ion acoustic kinetic Alfven (IAKA) solitary and rogue waves have been investigated in two temperature electrons magnetized superthermal plasma in the presence of dust impurity. A nonlinear analysis is carried out to derive the Korteweg-de Vries (KdV) equation using the reductive perturbation method (RPM) describing the evolution of solitary waves. The effect of various plasma parameters on the characteristics of the IAKA solitary waves is studied. The dynamics of ion acoustic kinetic Alfven rogue waves (IAKARWs) are also studied by transforming the KdV equation into nonlinear Schrodinger (NLS) equation. The characteristics of rogue wave profile under the influence of various plasma parameters ( $\kappa_{c}$ , $\mu_{c}$ , $\sigma $ , $\theta$ ) are examined numerically by using the data of Saturn’s magnetosphere (Schippers et al. 2008; Sakai et al. 2013).

Rogue-wave bullets in a composite (2+1)D nonlinear medium.

We show that nonlinear wave packets localized in two dimensions with characteristic rogue wave profiles can propagate in a third dimension with significant stability. This unique behavior makes these waves analogous to light bullets, with the additional feature that they propagate on a finite background. Bulletlike rogue-wave singlet and triplet are derived analytically from a composite (2+1)D nonlinear wave equation. The latter can be interpreted as the combination of two integrable (1+1)D models expressed in different dimensions, namely, the Hirota equation and the complex modified Korteweg-de Vries equation. Numerical simulations confirm that the generation of rogue-wave bullets can be observed in the presence of spontaneous modulation instability activated by quantum noise.

Rogue waves for Kadomstev-Petviashvili solutions in a warm dusty plasma with opposite polarity

Kadomstev-Petviashvili (KP) equation is derived using reductive perturbation method. This equation transformed into a nonlinear Schrodinger equation (NLS) by using appropriate variable transformations. When the carrier wave frequency is much smaller than the dust plasma frequency, the DA waves generating modulated wave packets in the form of rogue waves. The dependence of rogue wave profile on system plasma parameters investigated numerically. The parameters in this model are within the ranges corresponding to upper mesosphere, cometary tails and Jupiter’s magnetosphere.

Dust-acoustic waves modulational instability and rogue waves in a polarized dusty plasma

The polarization force-induced changes in the dust-acoustic waves (DAWs) modulational instability (MI) are examined. Using the reductive perturbation method, the nonlinear Schrödinger equation that governs the MI of the DAWs is obtained. It is found that the effect of the polarization term R is to narrow the wave number domain for the onset of instability. The amplitude of the wave envelope decreases as R increases, meaning that the polarization force effects render weaker the associated DA rogue waves. The latter may therefore completely damp in the vicinity of R ∼ 1, i.e., as the polarization force becomes close to the electrostatic one (the net force acting on the dust particles becomes vanishingly small). The DA rogue wave profile is very sensitive to any change in the restoring force acting on the dust particles. It turns out that the polarization effects may completely smear out the DA rogue waves.

Effect of electron beam on the properties of electron-acoustic rogue waves

The properties of nonlinear electron-acoustic rogue waves have been investigated in an unmagnetized collisionless four-component plasma system consisting of a cold electron fluid, Maxwellian hot electrons, an electron beam and stationary ions. It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of rogue wave profiles and the associated electric field on the carrier wave number, normalized density of hot electron and electron beam, relative cold electron temperature and relative beam temperature are discussed. The results of the present investigation may be applicable in auroral zone plasma.

Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.