Integral relations for rogue wave formations of Gardner equation

Nonlinear Dynamics - Rogue wave structures can often be described by a set of rational solutions. These can be derived for physical systems satisfying various well-known nonlinear equations. We...     

Revisit of rogue wave solutions in the Yajima–Oikawa system

The general rogue wave solutions for the one-dimensional (1D) Yajima–Oikawa (YO) system are derived through Hirota’s bilinear method and the Kadomtsev–Petviashvili hierarchy reduction method. Different from the previous work, we improve the construction of the differential operators to save the complicated recursiveness and obtain the rogue wave solutions in a purely algebraic expression. Based on this simple expression, the new shape of the third-order rogue waves’ arrangement is found. Moreover, three types of fundamental rogue waves and the rogue wave patterns from second to fifth order are graphically illustrated. In particular, there exist \(N-1\) (\(2\le N \)) polygonal configurations of Nth-order rogue waves for the 1D YO system, which is proven to be related to the Yablonskii–Vorob’ev polynomial hierarchy.

     

Contrast of optical activity and rogue wave propagation in chiral materials

Nonlinear Dynamics - We report the contrast of optical activity and properties of nonparaxial optical rogue waves for the higher-order nonparaxial chiral nonlinear Schrödinger (NLS) equation....     

Deformation rogue wave to the (2+1)-dimensional KdV equation

Many neurological diseases are known to be caused by bifurcations induced by a change in the values of one or more regulating parameter of nervous systems. The bifurcation control may have potential applications in the diagnosis and therapy of these dynamical diseases. In this paper, a washout filter-aided dynamic feedback controller composed of the linear term and the nonlinear cubic term is employed to control the onset of Hopf bifurcation in the Morris–Lecar (M–L) neuron model with type I. It is shown that the linear term determines the location of the Hopf bifurcation, while the nonlinear cubic term regulates the criticality of the Hopf bifurcation, preventing it from occurring in a certain range of the externally applied current. The relationships among the externally applied current, the linear control gain and the reciprocal of the filter time constant are further systematically analyzed, which help to make the best choice from the feasible parameter space to achieve our control task. Simulation results are provided to illustrate the effectiveness of the proposed methods.     

Nonlinear dynamics of higher-order rogue waves in a novel complex nonlinear wave equation

Nonlinear Dynamics - A novel complex nonlinear wave equation was recently found by Mukherjee and Kundu (Phys. Lett. A 383:985–990, 2019) and shown that it possesses the first-order rogue...     

Multiple rogue wave,breather wave and interaction solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation

Nonlinear Dynamics - Based on a direct variable transformation, we obtain multiple rogue wave solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation, including...     

Dynamical analysis of position-controllable loop rogue wave and mixed interaction phenomena for the complex short pulse equation in optical fiber

Nonlinear Dynamics - This paper investigates the complex short pulse equation, which can govern the propagation of ultra-short pulse packets along optical fibers. From the known Lax pair of this...     

On different aspects of the optical rogue waves nature

Rogue waves are giant nonlinear waves that suddenly appear and disappear in oceans and optics. We discuss the facts and fictions related to their strange nature, dynamic generation, ingrained instability, and potential applications. We present rogue wave solutions to the standard cubic nonlinear Schrödinger equation that models many propagation phenomena in nonlinear optics. We propose the method of mode pruning for suppressing the modulation instability of rogue waves. We demonstrate how to produce stable Talbot carpets—recurrent images of light and plasma waves—by rogue waves, for possible use in nanolithography. We point to instances when rogue waves appear as numerical artefacts, due to an inadequate numerical treatment of modulation instability and homoclinic chaos of rogue waves. Finally, we display how statistical analysis based on different numerical procedures can lead to misleading conclusions on the nature of rogue waves.

     

Upstream jetting phenomenon in planar shock wave experiments with ceramic powders

Jetting along upstream impact direction was observed in the experiments that were designed to study the response of ceramic powder materials to planar shock loading generated by impact. The jet formed catastrophically above certain impact stress level at the center of the impacted area and perforated upstream metal cover and flyer plates. Experiments were conducted with different impact stress levels, powder particle sizes, and geometrical parameters. Consistently repeatable results were obtained and effects arising from particle size, initial porosity, impact stress, and reflected wave were assessed. A simple mechanism-based model is used to explain the formation of the jet and estimate the jet velocity.     

Analysis of characteristics of rogue waves for higher-order equations

Nonlinear Dynamics - For various nonlinear physical equations, we describe the features of their rogue waves using simplified forms of their intensities and also by finding ‘volumes’....     

Characteristics of rogue waves on a periodic background for the Hirota equation

We consider the rogue dn-periodic waves (the rogue wave solutions on the dn-periodic waves background) for the Hirota equation by using Darboux transformation. We take Jacobian elliptic function dn as a seed solution, which is modulationally unstable as regards long wave perturbations. Through nonlinearization of the Lax pair for Hirota equation, the corresponding periodic eigenfunctions are successfully obtained. Based on these periodic eigenfunctions, we further construct the solutions of the Lax pair equations with dn-periodic wave seed solutions. In addition, numerical simulations are presented to reveal the phenomena of these solutions under different parameters choices.     

Recent advances in wave energy converters based on nonlinear stiffness mechanisms

Wave energy is one of the most abundant renewable clean energy sources, and has been widely studied because of its advantages of continuity and low seasonal variation. However, its low capture efficiency and narrow capture frequency bandwidth are still technical bottlenecks that restrict the commercial application of wave energy converters (WECs). In recent years, using a nonlinear stiffness mechanism (NSM) for passive control has provided a new way to solve these technical bottlenecks. This literature review focuses on the research performed on the use of nonlinear mechanisms in wave energy device utilization, including the conceptual design of a mechanism, hydrodynamic models, dynamic characteristics, response mechanisms, and some examples of experimental verification. Finally, future research directions are discussed and recommended.

     

Theory of the shimmy phenomenon

The shimmy phenomenon is the appearance of angular self-excited vibrations of the carriage wheels. Such self-excited vibrations provide a serious safety hazard for motion, which explains the great interest of scientists in this phenomenon [1–6]. This problem is most serious for the aircraft fore wheels.