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’....     

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.     

Dynamics of some novel breather solutions and rogue waves for the PT-symmetric nonlocal soliton equations

Nonlinear Dynamics - Tuned mass dampers are useful devices for limiting vibrations in various machines. Their main advantage is that they can be used as add-on elements and do not require...     

Physical properties of the flow in the separation region for three-dimensional interaction of a boundary layer with a shock wave

In a supersonic stream we consider the three-dimensional flow in the plane of symmetry in the region of interaction of a boundary layer with a shock wave which arises ahead of an obstacle mounted on a plate. The principal characteristic of this flow is the penetration of a filament of the ideal fluid within the separation zone and the formation on the surface of the plate and obstacle of narrow segments with high pressures, high velocity gradients, and large heat transfer coefficients.Pressure distribution measurements were made, shadow and schlieren photos were taken, and photographs of the flow pattern on the surface were made using dye coatings and low-melting models. The basic physical characteristics of the separation flow are established. The independence of the separation zone length of the boundary layer thickness is shown. Local supersonic flows are detected in the separation region, flow regimes are identified as a function of the angle of encounter of the separating flow with the obstacles, characteristic flow zones in the interaction region are identified.Notation s coordinate of separation point on the plate - l length of separation zone - H obstacle height - d obstacle transverse dimension - u freestream velocity - velocity gradient on stagnation line of obstacle - b jet width - compression shock standoff from the body - p static pressure - p_* pressure at stagnation point on obstacle - density - viscosity coefficient - boundary-layer thickness - compression shock angle - effective angle of separation zone - setting angle of obstacle on plate - M Mach number - R Reynolds number - P Prandtl number