Dust-acoustic rogue waves in a nonextensive plasma

Modulational instability, generation, and evolution of rogue waves in the generalized fractional nonlinear Schrödinger equations with power-law nonlinearity and rational potentials

In this paper, we investigate several properties of the modulational instability (MI) and rogue waves (RWs) within the framework of the generalized fractional nonlinear Schrödinger (FNLS) equations with rational potentials. We derive the dispersion relation for a continuous wave (CW), elucidating the relationship between the wavenumber and the instability growth rate of the CW solution in the absence of potentials. This relationship is primarily influenced by the power parameter σ, the Lévy index α, and the nonlinear coefficient g. Our theoretical findings are corroborated by numerical simulations, which demonstrate that MI occurs in the focusing context. Furthermore, we study the RW generations in both cubic and quintic FNLS equations with two types of time-dependent rational potentials, which make both cubic and quintic NLS equations support the exact RW solutions. Specifically, we show that the introduction of these two potentials allows for the excitations of controllable RWs in the defocusing regime. When these two potentials become the time-independent cases such that the stable W-shaped solitons with non-zero backgrounds are generated in these cubic and quintic FNLS equations. Moreover, we consider the excitations of higher-order RWs and investigate the conditions necessary for their generations. Our analysis reveals the intricate interplay between the system parameters and the potential configurations, offering insights into the mechanisms that facilitate the emergence of higher-order RWs. Finally, we find the separated controllable multi-RWs in the defocusing cubic FNLS equation with time-dependent multi-potentials. This comprehensive study not only enhances our understanding of MI and RWs in the fractional nonlinear wave systems, but also paves the way for future research in related nonlinear wave phenomena.

From rogue wave solution to solitons

Using a generalized nonlinear Schrödinger equation, we investigate the transformation of a fundamental rogue wave solution to a collection of solitons. Taking the third-order dispersion, self-steepening, and Raman-induced self-frequency shift as the generalizing effects, we systematically observe how a fundamental rogue wave has an impact on its surrounding continuous wave background and reshapes its own characteristics while a group of solitons are created. Applying a local inverse scattering technique based on the periodization of an isolated structure, we show that the third-order dispersion and Raman-induced self-frequency shift generates a group of solitons in the neighborhood where the rogue wave solution emerges. Using a volume interpretation, we show that the self-steepening effect stretches the rogue wave solution by reducing its volume. Also, we find that with the Raman-induced self-frequency shift, a decelerating rogue wave generates a red-shifted Raman radiation while the rogue wave itself turns into a slow-moving soliton. We show that when third-order dispersion, self-steepening, and Raman-induced self-frequency shift act together on the rogue wave solution, each of these effects favor the rogue wave to generate a group of solitons near where it first emerges while the rogue wave itself also becomes one of these solitons.

Instability of modified Zakharov-Kuznetsov solitons in an inhomogeneous partially degenerate electron-ion magnetoplasma

Linear and nonlinear propagation characteristics of multidimensional drift ion-acoustic (IA) solitons are studied in an inhomogeneous partially degenerate electron-ion magnetoplasma. A modified Zakharov-Kuznetsov (mZK) equation is deduced, accounting for the longitudinal as well as the transverse dispersions. It is shown that the mZK equation admits a distinct solution, revealing excitation of a pulse-shaped soliton when the phase speed exceeds by the wave dispersion. For the instability condition of the waves, a novel growth rate (γ) is derived by modifying the standard small-k expansion scheme. The instability criterion, given for long-wavelength IA waves, has not been described elsewhere. Numerical analysis show that solitary pulses gain energy from the ion drift, involving into instability: it saturates with amplification of the unstable potentials. Similarly trapped electrons lead to unstable growth of the solitary waves by enhancing γ. This study is relevant to compact stars and to high-density facilities where density inhomogeneity ensues the unstable drift modes. The instability analysis is important in understanding anomalous diffusion, which reduces the lifespan (τ=γ^{-1}) of magnetically confined plasma.

Dust-Acoustic Rogue Waves in an Electron-Positron-Ion-Dust Plasma Medium

In this work, the modulational instability of dust-acoustic (DA) waves (DAWs) is theoretically studied in a four-component plasma medium with electrons, positrons, ions, and negative dust grains. The nonlinear and dispersive coefficients of the nonlinear Schrödinger equation (NLSE) are used to recognize the stable and unstable parametric regimes of the DAWs. It can be seen from the numerical analysis that the amplitude of the DA rogue waves decreases with increasing populations of positrons and ions. It is also observed that the direction of the variation of the critical wave number is independent (dependent) of the sign (magnitude) of q. The applications of the outcomes from the present investigation are briefly addressed.

Optical polarization rogue waves and their identifications

Optical rogue waves are a class of pulses with extremely large amplitudes, whose probability of occurrence unexpectedly deviates from Gaussian-law statistics. To date, the mechanisms of rogue wave generation are still debated: investigations are under way, exploring the statistics of various pulse dimensions across different physical domains. Although polarization is one of the fundamental parameters of optical rogue waves, its statistics have received little attention until recently. Here, we review recent process of the polarization-dependent properties of optical rogue waves in ultrafast optics. Based on a two-dimensional statistical model, we introduce the concept of optical polarization rogue waves. Specifically, we consider the frequency of generation of waves with freak or rogue state of polarization, with a probability of occurrence deviating from a normal distribution. We demonstrate three nonlinear optical laser systems: a partially mode-locked laser, a dissipative soliton laser, and supercontinuum generation within a highly nonlinear fiber. Further, we identify optical polarization rogue waves in nonlinear laser systems, and discuss their generation mechanisms. Related results reveal that optical polarization rogue waves are embedded in optical systems with a deteriorated degree of coherence, which originates from vector four-wave-mixing processes. Polarization-dependent investigations will provide additional insight for our understanding of optical rogue waves.

Discrete eigenmodes of filamentation instability in the presence of a q-nonextensive distribution

Discrete eigenmodes of the filamentation instability in a weakly ionized current-driven plasma in the presence of a q-nonextensive electron velocity distribution is investigated. Considering the kinetic theory, Bhatnagar-Gross-Krook collision model, and Lorentz transformation relations, the generalized longitudinal and transverse dielectric permittivities are obtained. Taking into account the long-wavelength limit and diffusion frequency limit, the dispersion relations are obtained. Using the approximation of geometrical optics and linear inhomogeneity of the plasma, the real and imaginary parts of the frequency are discussed in these limits. It is shown that in the long-wavelength limit, when the normalized electron velocity is increased the growth rate of the instability increases. However, when the collision frequency is increased the growth rate of the filamentation instability decreases. In the diffusion frequency limit, results indicate that the effects of the electron velocity and q-nonextensive parameter on the growth rate of the instability are similar. Finally, it is found that when the collision frequency is increased the growth rate of the instability increases in the presence of a q-nonextensive distribution.

Transmission of rogue wave signals through a modified Noguchi electrical transmission network

A distributed electrical transmission network with dispersive elements that consists of a large number of identical unit cells is considered. Using the reductive perturbation method in the semidiscrete limit, we show that the voltage for the network is described by a nonlinear Schrödinger (NLS) equation with an external linear potential. Using such a NLS equation, the propagation of the first- and second-order rogue waves in the system is predicted and analyzed quantitatively and qualitatively. The rogue waves are expected to propagate for the bandwidth frequencies where the network may exhibit modulational instability. The effects of relevant network parameters on the characteristics of the rogue wave parameters are investigated. We show how to manipulate the relevant network parameters as well as the propagating frequency either to amplify the propagation of the rogue waves through the network, or to prevent rogue waves from being amplified in the network under consideration.

Possibility of the existence of the rogue wave and the super rogue wave in granular matter

By using the traditional perturbation technique, a focusing nonlinear Schrödinger equation (NLSE) for the one-dimensional bead chain with the initial prestress is first obtained. The Peregrine soliton, called the rogue wave in the present paper, and the super rogue wave are investigated both numerically and analytically. It is noted that both the rogue wave and the super rogue wave do exist in the one-dimensional bead chain. The solutions from the NLSE can correctly describe the real rogue wave as well as the real super rogue wave in the limiting case of small amplitude. Both the rogue wave and the super rogue wave propagate in the granular bead chain as if they are solitary waves.

Interacting Multiscale Acoustic Vortices as Coherent Excitations in Dust Acoustic Wave Turbulence

In this work, using three-dimensional intermittent dust acoustic wave turbulence in a dusty plasma as a platform and multidimensional empirical mode decomposition into different-scale modes in the 2+1D spatiotemporal space, we demonstrate the experimental observation of the interacting multiscale acoustic vortices, winding around wormlike amplitude hole filaments coinciding with defect filaments, as the basic coherent excitations for acoustic-type wave turbulence. For different decomposed modes, the self-similar rescaled stretched exponential lifetime histograms of amplitude hole filaments, and the self-similar power spectra of dust density fluctuations, indicate that similar dynamical rules are followed over a wide range of scales. In addition to the intermode acoustic vortex pair generation, propagation, or annihilation, the intra- and intermode interactions of acoustic vortices with the same or opposite helicity, their entanglement and synchronization, are found to be the key dynamical processes in acoustic wave turbulence, akin to the interacting multiscale vortices around wormlike cores observed in hydrodynamic turbulence.

Formation of rogue waves from a locally perturbed condensate

The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable condensate background is the fundamental physical model that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.

Modulation of a compressional electromagnetic wave in a magnetized electron-positron quantum plasma

Amplitude modulation of a compressional electromagnetic wave in a strongly magnetized electron-positron pair plasma is considered in the quantum magnetohydrodynamic regime. The important ingredients of this study are the inclusion of the external strong magnetic field, Fermi quantum degeneracy pressure, particle exchange potential, quantum diffraction effects via the Bohm potential, and dissipative effect due to collision of the charged carriers. A modified-nonlinear Schödinger equation is developed for the compressional magnetic field of the electromagnetic wave by employing the standard reductive perturbation technique. The linear and nonlinear dispersions of the electromagnetic wave are discussed in detail. For some parameter ranges, relevant to dense astrophysical objects such as the outer layers of white dwarfs, neutron stars, and magnetars, etc., it is found that the compressional electromagnetic wave is modulationally unstable and propagates as a dissipated electromagnetic wave. It is also found that the quantum effects due to the particle exchange potential and the Bohm potential are negligibly small in comparison to the effects of the Fermi quantum degeneracy pressure. The numerical results on the growth rate of the modulation instability is also presented.

Rogue waves lead to the instability in GaN semiconductors

A new approach to understand the electron/hole interfaced plasma in GaN high electron mobility transistors (HEMTs). A quantum hydrodynamic model is constructed to include electrons/holes degenerate pressure, Bohm potential, and the exchange/correlation effect and then reduced to the nonlinear Schrödinger equation (NLSE). Numerical analysis of the latter predicts the rough (in)stability domains, which allow for the rogue waves to occur. Our results might give physical solution rather than the engineering one to the intrinsic problems in these high frequency/power transistors.

Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers

In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous LF model are derived via the n-fold variable-coefficient Darboux transformation. The solitons and earthwormons display the elastic collisions. It is found that the nonautonomous LF model admits the higher-order periodic rogue waves, composite rogue waves (rogue wave pair), and oscillating rogue waves, whose dynamics can be controlled by the inhomogeneous nonlinear parameters. Based on the second-order rogue wave, a diamond structure consisting of four first-order rogue waves is observed. In addition, the semirational solutions (the mixed rational-exponential solutions) of the nonautonomous LF model are obtained, which can be used to describe the interactions between the rogue waves and breathers. Our results could be helpful for the design of experiments in the optical fiber communications.

Anomalous sea surface structures as an object of statistical topography

By exploiting ideas of statistical topography, we analyze the stochastic boundary problem of emergence of anomalous high structures on the sea surface. The kinematic boundary condition on the sea surface is assumed to be a closed stochastic quasilinear equation. Applying the stochastic Liouville equation, and presuming the stochastic nature of a given hydrodynamic velocity field within the diffusion approximation, we derive an equation for a spatially single-point, simultaneous joint probability density of the surface elevation field and its gradient. An important feature of the model is that it accounts for stochastic bottom irregularities as one, but not a single, perturbation. Hence, we address the assumption of the infinitely deep ocean to obtain statistic features of the surface elevation field and the squared elevation gradient field. According to the calculations, we show that clustering in the absolute surface elevation gradient field happens with the unit probability. It results in the emergence of rare events such as anomalous high structures and deep gaps on the sea surface almost in every realization of a stochastic velocity field.

Observation of self-excited acoustic vortices in defect-mediated dust acoustic wave turbulence

Using the self-excited dust acoustic wave as a platform, we demonstrate experimental observation of self-excited fluctuating acoustic vortex pairs with ± 1 topological charges through spontaneous waveform undulation in defect-mediated turbulence for three-dimensional traveling nonlinear longitudinal waves. The acoustic vortex pair has helical waveforms with opposite chirality around the low-density hole filament pair in xyt space (the xy plane is the plane normal to the wave propagation direction). It is generated through ruptures of sequential crest surfaces and reconnections with their trailing ruptured crest surfaces. The initial rupture is originated from the amplitude reduction induced by the formation of the kinked wave crest strip with strong stretching through the undulation instability. Increasing rupture causes the separation of the acoustic vortex pair after generation. A similar reverse process is followed for the acoustic vortex annihilating with the opposite-charged acoustic vortex from the same or another pair generation.

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

It is shown that the dynamics of amplitude-modulated compressional dispersive Alfvénic (CDA) waves in a collisional megnetoplasma is governed by a complex Ginzburg-Landau (CGL) equation. The nonlinear dispersion relation for the modulational instability of the CDA waves is derived and investigated numerically. It is found that the growth rate of the modulational instability decreases (increases) with the increase of the normalized electron-ion collision frequency α (the plasma β). The modulational instability criterion for the CGL equation is defined precisely and investigated numerically. The region of the modulational instability becomes narrower with the increase of α and β, indicating that the system dissipates the wave energy by collisions, and a stable CDA wave envelope packet in the form of a hole will be a dominant localized pulse. For a collisionless plasma, i.e., α=0, the CGL equation reduces to the standard nonlinear Schrödinger (NLS) equation. The latter is used to investigate the modulational (in)stability region for the CDA waves in a collisionless magnetoplasma. It is shown that, within unstable regions, a random set of nonlinearly interacting CDA perturbations leads to the formation of CDA rogue waves. In order to demonstrate that the characteristics of the CDA rogue waves are influenced by the plasma β, the relevant numerical analysis of the appropriate nonlinear solution of the NLS equation is presented. The application of our investigation to space and laboratory magnetoplasmas is discussed.