Rogue wave

About: Rogue wave is a research topic. Over the lifetime, 2977 publications have been published within this topic receiving 70933 citations. The topic is also known as: freak wave & monster wave.

Kinetic Alfven solitary and rogue waves in superthermal plasmas

Abstract: We investigate the small but finite amplitude solitary Kinetic Alfven waves (KAWs) in low β plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter κ, plasma β, and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvenic, compressive solitons are supported. We then extend the study to examine kinetic Alfven rogue waves by deriving a nonlinear Schrodinger equation from the KdV equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermality whereas the opposite is true when the plasma β increases. The findings of this study may find applications to low β plasmas in astrophysical environments where particles are superthermally distributed.

Impact of electron trapping in degenerate quantum plasma on the ion-acoustic breathers and super freak waves

Abstract: The propagation of nonlinear ion-acoustic (IA) structures in a two-component plasma consisting of ‘classical’ ions and temperature degenerate trapped electrons is investigated. Using the reductive perturbation method, a nonlinear Schrodinger equation (NLSE) is obtained and the modulational instability (MI) of the ion acoustic waves (IAWs) is investigated. The regions of the stability and instability of the modulated structures are defined precisely depending on the MI criteria. The analytical solutions of the NLSE in the form of various types of freak waves, including the Peregrine soliton, the Akhmediev breather, and the Kuznetsov–Ma breather are examined. Moreover, the higher-order freak waves are presented. The characteristics of the rogue waves and their dependence on relevant parameters (the temperature of the degenerate trapped electrons and wavenumber) are investigated.

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

Abstract: We discuss the generation mechanism of fundamental rogue wave structures in $N$-component coupled systems, based on analytical solutions of the nonlinear Schr\"odinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the $N$-component coupled nonlinear Schr\"odinger equation. Furthermore, our results show that $N$-component coupled nonlinear Schr\"odinger systems may possess $N$ different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

Optical rogue waves for the inhomogeneous generalized nonlinear Schrödinger equation.

Abstract: We present optical rogue wave solutions for a generalized nonlinear Schrodinger equation by using similarity transformation. We have predicted the propagation of rogue waves through a nonlinear optical fiber for three cases: (i) dispersion increasing (decreasing) fiber, (ii) periodic dispersion parameter, and (iii) hyperbolic dispersion parameter. We found that the rogue waves and their interactions can be tuned by properly choosing the parameters. We expect that our results can be used to realize improved signal transmission through optical rogue waves.

Solving localized wave solutions of the derivative nonlinear Schrodinger equation using an improved PINN method

Abstract: The solving of the derivative nonlinear Schrodinger equation (DNLS) has attracted considerable attention in theoretical analysis and physical applications. Based on the physics-informed neural network (PINN) which has been put forward to uncover dynamical behaviors of nonlinear partial different equation from spatiotemporal data directly, an improved PINN method with neuron-wise locally adaptive activation function is presented to derive localized wave solutions of the DNLS in complex space. In order to compare the performance of above two methods, we reveal the dynamical behaviors and error analysis for localized wave solutions which include one-rational soliton solution, genuine rational soliton solutions and rogue wave solution of the DNLS by employing two methods, also exhibit vivid diagrams and detailed analysis. The numerical results demonstrate the improved method has faster convergence and better simulation effect. On the bases of the improved method, the effects for different numbers of initial points sampled, residual collocation points sampled, network layers, neurons per hidden layer on the second order genuine rational soliton solution dynamics of the DNLS are considered, and the relevant analysis when the locally adaptive activation function chooses different initial values of scalable parameters are also exhibited in the simulation of the two-order rogue wave solution.