Multimode soliton dynamics in perturbed ladder lattices.

The coupling effects among lateral mode, longitudinal mode and torsional mode of a launch vehicle cannot be taken into account in traditional dynamic analysis using lateral beam model and longitudinal spring-mass model individually. To deal with the problem, propellant analogy methods based on beam model are proposed and coupled mass-matrix of liquid propellant is constructed through additional mass in the present study. Then an integrated model of launch vehicle for free vibration analysis is established, by which research on the interactions between longitudinal and lateral modes, longitudinal and torsional modes of the launch vehicle can be implemented. Numerical examples for tandem tanks validate the present method and its necessity.

A survey of results and problems of soliton dynamics in dispersive and hyperbolic nonlinear PDE’s and the related spectral and scattering theory. I focus on the problem of large time behavior of the nonlinear Schrödinger equation, with both solitary and radiative waves appearing in the solution. The equations are nonintegrable in general and in arbitrary dimension. I will formulate the main conjectures relevant to soliton dynamics.

We study collisions of moving nonlinear-Schrödinger solitons with a PT-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and, in a more qualitative form, for dark ones. In the former case, an essential aspect of the approximation is that it must take into regard the intrinsic chirp of the soliton, thus going beyond the framework of the simplest quasi-particle description of the soliton's dynamics. Critical velocities separating reflection and transmission of the incident bright solitons are found by means of numerical simulations, and in the approximate semi-analytical form. An exact solution for the dark soliton pinned by the complex PT-symmetric dipole is produced too.

Broad-area semiconductor lasers naturally emits on several lateral modes even at injection currents very close to the threshold current. An external cavity terminated by an apodizing holographic grating has been used to favor the oscillation of only one longitudinal mode and one lateral mode. It is possible to obtain laser oscillation on two different wavelengths simultaneously by using a grating that contains two grating periods. The fabrication technique of the apodizing holographic grating is explained. The spectrally-resolved near-field intensity distributions are presented.

We document a field experiment in which a path to strongly interacting soliton gas dynamics is observed within an intermittently open/closed estuary. We show that the shallow estuary mouth acts as a low-pass filter for incoming ocean waves, damping energy within the swell frequency band (0.04–1 Hz) and allowing surf-zone generated infragravity waves (frequency band 0.004–0.04 Hz) to enter the semienclosed shallow lagoon formed near the estuary mouth. These long waves penetrate under highly nonlinear conditions with Ursell numbers consistent with multisoliton fission regimes. The 𝑘–𝜔 spectrum of the incident wave trains is consistent with solitonic kinematics, demonstrating that solitons are released by the fission of incoming infragravity waves at the lagoon entrance. Continuous injection of solitonic wave trains and intense wave-wave interactions enhanced by the shallow and gradually varying bathymetry within the estuary lagoon lead to a quasistationary soliton gas regime with a substantially increased probability of rogue wave occurrence compared with linear wave theory. The Korteweg-de Vries nonlinear Fourier transform reveals that nearly half of the measured signal energy is explained by solitonic modes, confirming the key role that solitons have in enhancing rogue wave emergence in natural coastal settings.

Using the quasi-particle approach, we studied the problem of the reflection of quadratic spatial solitons from an interface between two χ(2) media with slightly different linear and nonlinear properties. The possibility of soliton capture by an interface associated with nonlinear surface wave excitation is shown. The calculations are carried out for the well-known single as well as a novel type of multihump soliton, for which we obtain a new analytical expression in the nonlocal limit for the first time to our knowledge.

Relaxation of solitons in nonlinear Schrödinger equations with potential

Optical solitons in mode-locked fiber lasers and optical communication links have a wide range of applications. A crucial step in studying the transmission modes of optical solitons is to investigate the relationship between equation parameters and soliton evolution using deep learning techniques. However, current identification models have a limited parameter domain search range and are greatly influenced by initialization, often leading to divergence towards incorrect parameter values. This research harnesses reinforcement learning to revamp the iterative process of the parameter identification model. Through the development of a two-stage optimization strategy, the model is capable of conducting an accurate parameter search across arbitrary domains. The investigation encompasses a series of experiments on various standard and higher-order equations, illustrating that the innovative model overcomes the impact of initialization on the parameter search, and the identified parameters are guided towards their correct values. The enhanced model markedly improves experimental efficiency and holds significant promise for advancing the research of soliton propagation dynamics and addressing intricate scenarios.

We are constructing and studying a unicycle robot which balances and steers itself by swinging its pendulum sidewards. Our unicycle robot, automatic lateral-pendulum unicycle (ALP Cycle), has three main parts: wheel, chassis and pendulum. It is an underactuated robot with only two control inputs and five degrees of freedom. The wheel motor provides balancing torque in forward-backward direction while the pendulum motor provides balancing torque in the left-right direction. For balancing the ALP Cycle either from a non-upright static initial posture or from external disturbances, both the wheel and pendulum motors need to provide the necessary recovery torques to counter the falling motion of ALP Cycle's bodies in two directions. In this paper, we discuss qualitatively the issues of balancing of ALP Cycle including the different types of static initial postures which pose different difficulty levels. Next, three linear controllers are designed for longitudinal and lateral modes for balancing ALP Cycle based on the idea of separate regulations. The performances of the controllers for different initial postures are evaluated by numerical simulation in MATLAB.

Due to the weak birefringence from the intracavity fiber, vector solitons are easily generated in GHz-fundamental-repetition-rate mode-locked fiber lasers, which can exhibit diverse time-varying polarization dynamics. These soliton dynamics can lead to polarization instability of the pulse train, which prevents industrial and scientific applications that require stable and uniform pulse trains. However, it is hard to suppress the polarization instability due to insufficient space for inserting traditional polarizers and difficulties in enhancing the fiber birefringence in the ultrashort fiber laser cavity. To this end, here we propose an alternative method that can effectively transform the vector solitons into scalar solitons by exploring gold nanorod (GNR) film as a polarizer in the laser cavity. First, the theoretical studies of polarization dynamics in ultrashort Fabry–Pérot (FP) fiber lasers with and without intracavity GNR film are conducted. The results indicate that the use of GNR film can significantly suppress the polarization instability and generate scalar solitons. Then, the large-scale preparation of GNRs with longitudinal surface plasmon resonance absorption peak of >1380 nm is realized by a two-step seed-mediated method, and the GNR film with an operation wavelength range covering the C + L band is fabricated by electrospinning. Finally, we apply the GNR film to a 2-cm-long FP fiber laser, and convert polarization rotation vector solitons to linearly polarized solitons (LPSs) at 1.5 μm. The polarization extinction ratio of the improved LPS pulse train is up to 33 dB.

SummaryA nonlinear MIMO controller based on the conditional integrator technique is designed for the robust stabilization of a new satellite launching strategy called (unmanned) airlaunch. This control technique concerns an integrator performing similar to a sliding mode controller when the system is outside a boundary layer defined by the controller, and performing as a linear controler that provides the integral term when the system enters into the boundary layer. Satellite airlaunch strategy consists in using a two‐stage launching system. The first stage is composed of an airplane (manned or unmanned) that carries a rocket launcher, which constitute the subsequent stages. The control objective is to stabilize the aircraft in the launch phase. It is developed separately for the two nonlinear (one MIMO and one SISO) motion modes of the model, the longitudinal mode and lateral mode, and is then applied to the full model of the aircraft. The considered system is highly nonlinear, mostly as a consequence of a possible large angle of attack, sideslip, and roll angle. Finally, the present work illustrates through simulations, the good performance of the proposed control algorithm. Copyright © 2013 John Wiley & Sons, Ltd.

Nanoscale lasers are the key component in the integrated photonics chips and have attracted much interests. Nanoblets and nanowires lasers, as one of the candidates for the nanoscale lasers, have been developed for one more decades. Many kinds of nanowire lasers with different functionalities, such as wavelength tunable, single mode, polarized emission and so on, have been demonstrated. However, the reported single mode nanowire lasers are mostly realized through microfabrication process, careful manipulation and complicated structures. Here, we present a new type of lateral emission single mode nanobelt lasers with high polarization ratio which are fabricated by the one step traditional VLS (Vapor Liquid Solid) growth. Different from the traditional nanobelt lasers which are based on the FP cavity formed in the longitudinal direction, the emission of this novel nanoblet laser is lateral which is contribute to the special wire-like structures grown on the nanobelt. It shows band edge emission and the wavelength is centered at 712.6 nm with linewidth about 0.18 nm. The threshold reach as low as 15 uJ/cm2 benefit from the unique morphology which provides enhanced confinement factor for optical modes. Meanwhile the laser emission is highly polarized with polarization ration as high as 0.91. This lateral emission single mode nanobelt laser with high polarization ratio, low threshold and simple fabrication technique offers an economic and effective choice to the future optical applications.

In this research, a finite element model is established to investigate effective seismic control schemes for a self-anchored suspension bridge (SASB) with three towers. Nonlinear dynamic analyses are conducted to evaluate the seismic performance of SASB with different layout schemes of viscous dampers and buffers, which were installed in longitudinal direction and transversal direction, respectively. The responses of the SASB designed with 10 seismic control schemes are compared to ascertain suitable seismic schemes for SASBs. The results show that the number and location of lateral buffers have an important impact on the dynamic characterization of the SASB, especially for the first lateral mode and lateral fundamental frequency. To effectively increase the seismic performance of SASBs with three towers, mounting buffers between the side towers and the main girder of SASBs is an appropriate scheme. The viscous dampers can effectively decrease the dynamic reaction of the towers and longitudinal deformation of the girder under earthquake excitations. The plan involves the installation of dampers between the main concrete stiffening girder and the side towers as the optimal longitudinal seismic scheme for the SASB. The study offers important insights into the seismic design of SASBs with three towers.

Cyclotron and Cherenkov resonant interactions between a radially confined electron beam spiraling in a magnetoplasma and a quasi-monochromatic lower hybrid wave are considered. The main physical process consists of the nonlinear self-organization of part of the beam electrons, forming dynamically stable bunches that are continuously decelerated or accelerated while keeping resonance with the emitted wave. For the Cherenkov and anomalous Doppler resonances, such bunches exist during an infinitely long time; the main difference between both cases is that, for the cyclotron resonance, the gain of energy supplied by the longitudinal motion of the beam electrons is mainly spent to increase their perpendicular energy, and only a small part of it, proportional to the ratio of the wave frequency to the electron gyrofrequency, is given for wave radiation. For the normal Doppler resonance case, electron bunches also appear during the nonlinear wave-particle evolution. However, electrons lose perpendicular energy and are accelerated along the longitudinal direction. As formed bunches do not have a high stability, the interaction of the beam electrons with the wave weakens rather quickly, whereas the wave radiation decreases as a function of the distance from the injector.

In this study, a new ultrasonic wave based imaging techniques developed using longitudinal ultrasonic waves for detecting defects in pipeline structures. Ultrasonic waves are gaining popularity for pipeline monitoring because of its sensitivity to small defects and a long sensing range. Based on the merits of the ultrasonic waves, several research groups have developed ultrasonic wave based imaging techniques for pipeline monitoring. Conventionally, a pure torsional mode is often generated using shear-mode piezoelectric transducers or electromagnetic acoustic transducers (EMAT) and used for pipe damage detection. In this study, a new ultrasonic wave based imaging technique is developed using a longitudinal wave mode instead of the pure torsional mode. The longitudinal mode is generated using inexpensive macro fiber composite (MFC) transducers attached at one end of the pipe, eliminating the need for the shear-mode transducers or EMATs. Then, the reflections generated by the interaction of the incident longitudinal mode with a defect are measured in a pulse echo manner. Using a normal mode expansion technique, flexural modes are extracted from the reflected signals. When a defect-induced reflected wave mode is propagated back along the longitudinal direction of the pipe, its dispersive nature is minimized and best-compensated at the defection location. Therefore, by virtually propagating each defect-induced flexural mode back in the wave propagation direction, an image which visualizes the focusing of the back-propagated flexural modes can be obtained and the defect location can be identified. Numerical simulations and experimental tests are conducted to demonstrate that a wall-thinning in a steel pipe can be detected and quantified using the proposed imaging technique.