Exciting rogue waves,breathers, and solitons in coherent atomic media

We propose a scheme that excites rogue waves via electromagnetically induced transparency(EIT), which can also excite breathers and solitons. The system is a resonant Λ-type atomic ensemble. Under EIT conditions, the envelope equation of the probe field can be reduced to several different models, such as the saturable nonlinear Schr?dinger equation(SNLSE), and SNLSE with the trapping potential provided by a far-detuned laser field or a magnetic field. In this scheme, rogue waves can be generated by different initial pulses, such as the Gaussian wave with(or without) the uniform background. The scheme can be used to obtain rogue waves,breathers and solitons. We show the existence regions of rogue waves, breathers, and solitons as the function of the amplitude and width of the initial pulse. The novelty of our paper is that, we not only show rogue waves in the integrable system numerically, but also present the method to generate and control rogue waves in the non-integrable system.     

Nonlinear stage of development of high-frequency instability of electromagnetic waves in flux-magnetoactive plasma system

Scientific-Research Institute of Radiophysics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 9, pp. 1036–1041, September, 1988.     

Nonlinear coherent transport of waves in disordered media

We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and we corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios such as scattering of light in a nonlinear Kerr medium or propagation of matter waves in disordered potentials.     

Modulational instability,rogue waves,and envelope solitons in opposite polarity dusty plasmas

Dust-acoustic (DA) waves (DAWs) and their modulational instability (MI) have been investigated theoretically in a plasma system consisting of inertial opposite polarity (positively and negatively) warm adiabatic charged dust grains as well as inertialess non-extensive $q?$distributed electrons and non-thermal ions. A nonlinear Schrödinger equation (NLSE) is derived by using the reductive perturbation method. It has been observed from the analysis of NLSE that the modulationally stable solitary DAWs give rise to the existence of dark envelope solitons, and that the modulationally unstable solitary DAWs give rise to the existence of bright envelope solitons or rogue structures. It is also observed for the fast mode of DAWs that the basic features (viz. stability of the DAWs, MI, growth rate, amplitude, and width of the DA rogue waves, etc.) are significantly modified by the related plasma parameters (viz. dust masses, dust charge state, non-extensive parameter q, and non-thermal parameter α). The results of our present investigation might be useful for understanding different nonlinear electrostatic phenomena in both space (viz. ionosphere and mesosphere) and laboratory plasmas (viz. high intensity laser irradiation and hot cathode discharge).     

Energy portrait of rogue waves

Processes of the concentration of energy at the formation of rogue waves have been studied in computer experiments based on the exact hydrodynamic equations for an ideal fluid. The distribution of anomalies of waves both in height and in energy has been found in the computer experiment. Correlation between the energy concentration and height of anomalously large surface waves has been revealed. The results can be used to estimate the danger of anomalously large surface waves.     

A swirling jet with vortex breakdown: three-dimensional coherent structures

The paper reports on shape of a three-dimensional coherent structure in a velocity field of a high-swirl turbulent jet with the bubble-type vortex breakdown. A set of the 3D instantenous velocity fields was measured by using the tomographic particle image velocimetry (tomographic PIV) technique and processed by the proper orthogonal decomposition (POD) method. The detected intensive coherent velocity component corresponded to a helical vortex core of the swirling jet and two secondary spiral vortices. The entire coherent structure was rotating around the jet axis in compliance with the direction of the flow swirl. From the 3D data it is concluded that the dynamics of the strsucture can be described by a traveling wave equation: Re[A(y, r)·e ^{i(mθ + ky - ωt)}] with the number of the spiral mode m = +1 for positively defined k and ω.     

Modulation instability,rogue waves and conservation laws in higher-order nonlinear Schrodinger equation

In this paper,the modulation instability(MI),rogue waves(RWs)and conseryation laws of the coupled higher-order nonlinear Schrodinger equation are investigated.According to MI and the 2×2 Lax pair,Darboux-dressing transformation with an asymptotic expansion method,the existence and properties of the one-,second-,and third-order RWs for the higher-order nonlinear Schrodinger equation are constructed.In addition,the main characteristics of these solutions are discussed through some graphics,which are draw widespread attention in a variety of complex systems such as optics,Bose-Einstein condensates,capillary fow,superfluidity,fluid dynamics,and finance.In addition,infinitely-many conservation laws are established.     

Rogue waves at low Benjamin-Feir indices: Numerical study of the role of nonlinearity

The nonlinear interaction between waves in incoherent sea states is weaker than their dispersion. In this situation, random space-time focusing is the main mechanism of the formation of rogue waves. The numerical simulation has indicated that nonlinearity becomes important at the final stage of focusing and can significantly change predictions of the so-called second-order theory concerning the parameters of rogue waves. The elongation of the crest of a rogue wave as compared to that predicted by the second-order theory is an important effect promoting the “weighting of the tails” of the distribution function of the vertical deviation of the free surfaces.     

Modulation instability,rogue waves and conservation laws in higher-order nonlinear Schrödinger equation

In this paper, the modulation instability(MI), rogue waves(RWs) and conservation laws of the coupled higher-order nonlinear Schr?dinger equation are investigated. According to MI and the2?×?2 Lax pair, Darboux-dressing transformation with an asymptotic expansion method, the existence and properties of the one-, second-, and third-order RWs for the higher-order nonlinear Schr?dinger equation are constructed. In addition, the main characteristics of these solutions are discussed through some graphics, which are draw widespread attention in a variety of complex systems such as optics, Bose–Einstein condensates, capillary flow, superfluidity, fluid dynamics,and finance. In addition, infinitely-many conservation laws are established.     

Extreme waves that appear from nowhere: On the nature of rogue waves

We have numerically calculated chaotic waves of the focusing nonlinear Schrr?odinger equation (NLSE), starting with a plane wave modulated by relatively weak random waves. We show that the peaks with highest amplitude of the resulting wave composition (rogue waves) can be described in terms of exact solutions of the NLSE in the form of the collision of Akhmediev breathers.     

Evolution of three-dimensional coherent structures in compressible axisymmetric jet

A high order difference scheme is used to simulate the spatially developing compressible axisymmetric jet. The results show that the Kelvin-Helmholtz instability appears first when the jet loses its stability, and then with development of jet the increase in nonlinear effects leads to the secondary instability and the formation of the streamwise vortices. The evolution of the three-dimensional coherent structure is presented. The computed results verify that in axisymmetric jet the secondary instability and formation of the streamwise vortices are the important physical mechanism of enhancing the flow mixing and transition occurring.     

Nonlinear model for coherent electric field structures in the magnetosphere

A new pseudo-three-dimensional electron hole in a magnetized plasma is possible when the low-frequency ion dynamics is taken into account. The newly found nonlinear Bernstein-Greene-Kruskal stationary solution, whose parallel phase velocity ranges between almost zero and the electron thermal speed, has the form of a cylinder that is tilted relative to the magnetic field. These structures are interpreted as three-dimensional electron holes coupled with hydrodynamic vortices, and provide a possible theoretical explanation for the POLAR and FAST satellite observations of coherent structures characterized by bipolar spikes of the parallel electric field and large perpendicular ion kinetic energies.     

High-order rogue waves for the Hirota equation

The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures.     

Evaluating the robustness of rogue waves under perturbations

Rogue waves, and their periodic counterparts, have been shown to exist in a number of integrable models. However, relatively little is known about the existence of these objects in models where an exact formula is unattainable. In this work, we develop a novel numerical perspective towards identifying such states as localized solutions in space-time. Importantly, we illustrate this methodology for different perturbations of nonlinear Schrödinger models. In particular, in addition to benchmarking known solutions (and confirming their numerical propagation under controllable error) this enables the continuation of such solutions over parametric variations to non-integrable models. As a result, we can answer in the positive the question about the parametric robustness of Peregrine-like waveforms and even of generalizations thereof on a cnoidal wave background.     

非自治物质畸形波的传播操控

研究了(1+1)维的变系数Gross-Pitaevskii方程, 获得了该方程的精确畸形波解. 基于该精确畸形波解, 深入研究了非自治物质畸形波在随时间指数变化的相互作用下的传播动力学行为, 发现非自治畸形波除具有“来无影、去无踪”的不可预测特性外, 也可实现完全激发、抑制激发以及维持激发等操控. 研究表明, 畸形波操控的关键是对累积时间的最大值T_max 与峰值位置T₀ (或T_I,T_II)值大小关系的调节. 当T_max > T₀ (或T_I,T_II)时畸形波被快速地完全激发, 热原子团中的原子增加到凝聚体中. 当T_max = T₀ (或T_I,T_II) 时畸形波激发到最大振幅, 可以维持相当长的时间而不消失, 热原子团中的原子增加到凝聚体中. 当T_max < T₀ (或T_I,T_II)时畸形波没有充足的时间来激发而被抑制甚至消失, 凝聚体中的原子减少. 这些结果在理论和实际应用上具有启迪意义.     

Generation of surface waves by three-dimensional vortex structures

The oblique interactions of vortex rings with a free surface is discussed. The signature of a submerged turbulent jet on a free surface is presented.     

Multiscale coherent structures and broadband waves due to parallel inhomogeneous flows

Linear theory analysis and particle-in-cell simulations show that a spatial transverse gradient in the ion drift parallel to the magnetic field, dV(di)/dxOmega(i). Nonlinearly, these waves lead to multiscale spatially coherent structures, substantial cross-field transport, ion energization, and phase-space diffusion. Large spikes are formed in the parallel electric field time series. These signatures are similar to the Fast Auroral Snapshot satellite observations in the upward current region.     

Controllable optical rogue waves: Recurrence, annihilation and sustainment

We investigate optical rogue waves in nonlinear optical fiber with group-velocity dispersion, cubic nonlinearity and linear gain managements. We present conditions for controlling the dynamics of optical pulses via a lens-type transformation. By properly choosing the distributed coefficients, we demonstrate analytically that rogue waves can be restrained or even be annihilated, emerge periodically and sustain forever. We also figure out the center-of-mass motion of rogue waves.     

Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces

We experimentally demonstrate the significance of the longitudinal-transverse coupling in the mesoscopic regime by using a high-Q laser resonator as an analog experiment. The longitudinal-transverse coupling is found to lead to the three-dimensional (3D) coherent waves that are localized on the parametric surfaces with Lissajous transverse patterns. More strikingly, experimental results reveal that the mode locking of the 3D coherent states forms a nearly complete Devil's staircase with the hierarchical ordering.