Shape-changed propagations and interactions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluids

In this article, we consider the(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP)equation in fluids. We show that a variety of nonlinear localized waves can be produced by the breath wave of the GKP model, such as the(oscillating-) W-and M-shaped waves, rational W-shaped waves, multi-peak solitary waves,(quasi-) Bell-shaped and W-shaped waves and(quasi-) periodic waves. Based on the characteristic line analysis and nonlinear superposition principle, we give the transition conditions analytically. We find the interesting dynamic behavior of the converted nonlinear waves, which is known as the time-varying feature. We further offer explanations for such phenomenon. We then discuss the classification of the converted solutions. We finally investigate the interactions of the converted waves including the semi-elastic collision, perfectly elastic collision, inelastic collision and one-off collision. And the mechanisms of the collisions are analyzed in detail. The results could enrich the dynamic features of the high-dimensional nonlinear waves in fluids.     

考虑量子效应的Zakharov方程组的孤波解

借助Maple程序，利用扩展的双曲函数法和双函数法求解了考虑量子效应的Zakharov方程组，得到了多种孤波解，其中包括亮孤波解、W型孤波解、M型孤波解和奇性孤波解. 关键词： 量子效应 Zakharov方程组 扩展的双曲函数法 孤波解     

Multi-Solitons and Combined Solitons with Self-Similar Behaviors in a Birefringent Fiber with Higher-Order Effects

A coupled variable-coefficient higher-order nonlinear Schr(o|¨)dinger equation in biretringent fiber is studied,and analytical multi-soliton,combined bright and dark soliton,W-shaped and M-shaped soliton solutions are obtained.Nonlinear tunnelling of these combined solitons in dispersion barrier and dispersion well on an exponential background is discussed,and the decaying or increasing,even lossless tunnelling behaviors of combined solitons are decided by the decaying or increasing parameter.     

Soliton molecules and mixed solutions of the(2+1)-dimensional bidirectional Sawada-Kotera equation

In this paper, we investigate some new interesting solution structures of the(2+1)-dimensional bidirectional Sawada–Kotera(bSK) equation. We obtain soliton molecules by introducing velocity resonance. On the basis of soliton molecules, asymmetric solitons are obtained by changing the distance between two solitons of molecules. Based on the N-soliton solutions,several novel types of mixed solutions are generated, which include the mixed breather-soliton molecule solution by the module resonance of the wave number and partial velocity resonance,the mixed lump-soliton molecule solution obtained by partial velocity resonance and partial long wave limits, and the mixed solutions composed of soliton molecules(asymmetric solitons), lump waves, and breather waves. Some plots are presented to clearly illustrate the dynamic features of these solutions.     

Quantum key distribution using the localized soliton pulses via a wavelength router in the optical network

We propose a new system of a continuous variable quantum key distribution via a wavelength router in the optical networks. A large bandwidth signal is generated by a soliton pulse propagating within the micro ring resonator, which is allowed to form the continuous wavelength with large tunable channel capacity. There are two forms of localized soliton pulses proposed. Firstly, the required information is transmitted via the localized temporal soliton pulse. Secondly, the continuous variable quantum key distribution is formed by using the localized spatial soliton pulse via a quantum router and networks, which is formed by using and optical add/drop multiplexer incorporating in the network. The localized soliton pulses are available for add/drop signals to/from the optical network, where the high security and capacity information can be performed.     

Optical Rogue Wave Excitation and Modulation on a Bright Soliton Background

We study rogue waves in an inhomogeneous nonlinear optical fiber with variable coefficients.An exact rogue wave solution that describes rogue wave excitation and modulation on a bright soliton pulse is obtained.Special properties of rogue waves on the bright soliton,such as the trajectory and spectrum,are analyzed in detail.In particular,our analytical results suggest a way of sustaining the peak shape of rogue waves on the soliton background by choosing an appropriate dispersion parameter.     

Soliton generation via continuous stokes acoustic self-scattering of hypersonic waves in a paramagnetic crystal

A new mechanism is proposed for continuous frequency down-conversion of acoustic waves propagating in a paramagnetic crystal at a low temperature in an applied magnetic field. A transverse hypersonic pulse generating a carrier-free longitudinal strain pulse via nonlinear effects is scattered by the generated pulse. This leads to a Stokes shift in the transverse hypersonic wave proportional to its intensity, and both pulses continue to propagate in the form of a mode-locked soliton. As the transverse-pulse frequency is Stokes shifted, its spectrum becomes narrower. This process can be effectively implemented only if the linear group velocity of the transverse hypersonic pulse equals the phase velocity of the longitudinal strain wave. These velocities are renormalized by spin-phonon coupling and can be made equal by adjusting the magnitude of the applied magnetic field. The transverse structure of the soliton depends on the sign of the group velocity dispersion of the transverse component. When the dispersion is positive, planar solitons can develop whose transverse component has a topological defect of dark vortex type and longitudinal component has a hole. In the opposite case, the formation of two-component acoustic “bullets” or vortices localized in all directions is possible.     

Ultrashort light pulses generated from modulation instability: background removal and soliton content

Modulation instability can be used to convert a continuous light wave into a train of pulses on a constant background. It is a longstanding discussion whether these pulses can be converted into solitons. We clarify the situation by using a more general mathematical context, invoking the Akhmediev breather, Peregrine soliton and Kuznetsov-Ma soliton solutions of the wave equation, and suggest the use of a Mach–Zehnder interferometer to remove the background. Expressions for the pulse widths and peak powers thus obtained are presented, and their soliton content is determined. It turns out that more than 95 % of each pulse’s energy can be converted to a soliton.     

Localized Optical Waves in Defocusing Regime of Negative-Index Materials

We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schrodinger equation with self-steepening effect. Important characteristics of localized waves,such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intriguing sequential transition that involves the rogue wave, antidark-dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is established in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.     

A novel system of the simultaneous trapping of dark-bright solitons within a nano-waveguide system

We propose a novel system of a nano-waveguide that can be used to generate the continuous spectrum, i.e. white light. The simultaneous trapping and generation of short and millimeter waves can also be performed by using either bright or dark soliton. A system consists of two micro- and a nano-ring resonators that can be integrated into a single system. The large bandwidth is generated by a soliton pulse within a Kerr-type nonlinear medium where the continuous bandwidth or wavelength can be performed. The simultaneous dark-bright solitons conversion is performed and achieved. Results obtained have shown the potential of using the technique for continuing light spectra generation, where the filtering signals are allowed by using the suitable device parameters. The advantage is that the large bandwidth separation of the short and sub-millimeter waves can be obtained, which is allowed to form the simultaneous generation of short and millimeter waves within a single system. Further, light pulse can be trapped within a nano-waveguide, which is available to form the memory device.     

Observation of dipole-mode vector solitons

We report on the first experimental observation of a novel type of optical vector soliton, a dipole-mode soliton, recently predicted theoretically. We show that these vector solitons can be generated in a photorefractive medium employing two different processes: a phase imprinting, and a symmetry-breaking instability of a vortex-mode vector soliton. The experimental results display remarkable agreement with the theory, and confirm the robust nature of these radially asymmetric two-component solitary waves.     

Multi-soliton generation with extremely narrow free spectrum range for multiplexed sensors via optical network

We propose a new system of multiplexer sensors using the localized soliton pulse generated by a microring resonator in optical networks. A large bandwidth signal is generated by a soliton pulse propagating within the microring resonator, which is allowed to form the multiplexed sensors. Two forms of soliton pulses are generated and localized, i.e. temporal and spatial solitons. The required soliton pulses with specified wavelengths can be localized and formed the sensing. This is formed by using an optical add/drop multiplexer incorporating in the optical network, where the localized soliton pulses are available for add/drop signals to/from the optical network. The change in physical parameter measured the change in soliton wavelength, which formed the measurement.     

Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers

We present the theory of electrostrictional interaction of soliton pulses in optical fibers. Solitons excite acoustic waves propagating in the direction transverse to the fiber axis. Scattering of optical radiation on these waves leads to a timing jitter of the optical pulses arrival time. We consider this effect as nonlinear self-scattering of light on acoustic waves. Because of the fact that a value of acoustic lifetime can reach a value of about 100 ns self-scattering on acoustic waves can be observed for a single optical pulse as well as for an optical pulse sequence as a whole. The value of single soliton self-frequency shift due to excitation of acoustic waves as a function of soliton duration have been obtained. For soliton duration _sol > 14 ps an acoustic wave soliton self-frequency shift is larger than the Raman soliton self-frequency shift.The obtained theoretical results describe well the long-range interaction of soliton pulse trains in an optical fiber. The value of bit error rate due to electrostrictional interaction of optical pulses in high bit rate, ultra long soliton communication systems have been obtained.     

Soliton Molecules,Asymmetric Solitons and Hybrid Solutions for(2+1)-Dimensional Fifth-Order Kd V Equation

Soliton molecules were first discovered in optical systems and are currently a hot topic of research. We obtain soliton molecules of the(2+1)-dimensional fifth-order Kd V system under a new resonance condition called velocity resonance in theory. On the basis of soliton molecules, asymmetric solitons can be obtained by selecting appropriate parameters. Based on the N-soliton solution, we obtain hybrid solutions consisting of soliton molecules,lump waves and breather waves by partial velocity resonance and partial long wave limits. Soliton molecules,and some types of special soliton resonance solutions, are stable under the meaning that the interactions among soliton molecules are elastic. Both soliton molecules and asymmetric solitons obtained may be observed in fluid systems because the fifth-order Kd V equation describes the ion-acoustic waves in plasmas, shallow water waves in channels and oceans.     

非对称耦合两层可激发介质中的螺旋波动力学

本文采用Bär-Eiswirth模型研究了两层可激发介质中螺旋波的动力学, 两层介质采用抑制和兴奋性非对称耦合. 数值模拟结果表明: 兴奋性非对称耦合可以促进两个不同频率的螺旋波锁频, 即使初始频率相差大, 两螺旋波也能实现锁频, 这种耦合使两个螺旋波具有最强的锁频能力; 当两层介质采用抑制性非对称耦合时, 只有当两个初始螺旋波的频率差比较小才能实现锁频, 而且比一般扩散耦合的锁频范围窄, 两螺旋波锁频能力达到最低水平; 当耦合强度和控制参数适当选取时, 抑制性和兴奋性非对称耦合既可以使其中一层介质维持螺旋波态, 使另一层介质中的螺旋波演化到静息态或低频靶波态, 也可以使两层介质中的螺旋波都漫游, 或都转变成靶波, 最后这两个靶波要么消失, 要么转变成平面波状的振荡斑图, 而且两层介质振荡是反相的, 此外在模拟中还观察到两螺旋波局部间歇锁频现象, 这些结果有助于人们理解在心脏系统中出现的复杂现象.     

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.     

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic–quintic nonlinear Schr o¨dinger(CCQNLS) equations through the generalized Darboux transformation(DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higherorder localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions;(ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons;(iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α.These results further uncover some striking dynamic structures in the CCQNLS system.     

Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths

Stochastic numerical simulations are used to study the statistical properties of supercontinuum spectra generated in photonic crystal fibre with two zero dispersion wavelengths. For picosecond pulse excitation, we examine how the statistical properties of solitons generated on the long wavelength edge of the supercontinuum (``optical rogue waves") are modified by energy transfer to dispersive waves across the second zero dispersion wavelength. The soliton statistics (characterized in terms of peak power, wavelength and pulse duration) are shown to be strongly modified by the mechanism of dispersive wave generation, with the detailed form of the probability distribution depending strongly on input pulse energy.     

非线性色散渐减光纤中高峰值脉冲的激发和传输

本文基于变系数的非线性薛定谔方程,数值地讨论高峰值脉冲在色散渐减光纤中的激发和传输。首先,基于变系数非线性薛定谔方程的Peregrine孤子解,解析和数值地讨论精确的Peregrine孤子在色散渐减光纤中的传输特性。其次,通过输入不同的平面波背景上的局域脉冲,研究高峰值脉冲在非线性色散渐减光纤中的激发和传输。结果显示Peregrine孤子在色散渐减光纤中传输时,会产生一个空间和时间都局域化的高峰值单脉冲,并且当啁啾为负时,脉冲的幅值增加,脉宽被压缩。若光纤系统存在增益,脉冲的幅值也会增加。由于非线性光纤中的调制不稳定性过程,不同平面波背景上的小局部扰动都可激发出高峰值脉冲,除了峰值和宽度略有不同外,激发脉冲的形状几乎相同。     

Underwater asymmetric acoustic transmission structure using the medium with gradient change of impedance

We propose an underwater asymmetric acoustic transmission structure comprised of two media each with a gradient change of acoustic impedance. By gradually increasing the acoustic impedances of the media, the propagating direction of the acoustic wave can be continuously bent, resulting in allowing the acoustic wave to pass through along the positive direction and blocking acoustic waves from the negative one. The main advantages of this structure are that the asymmetric transmission effect of this structure can be realized and enhanced more easily in water. We investigate both numerically and experimentally the asymmetric transmission effect. The experimental results show that a highly efficient asymmetric acoustic transmission can be yielded within a remarkable broadband frequency range, which agrees well with the numerical prediction. It is of potential practical significance for various underwater applications such as reducing vibration and noise.