一类耦合非线性波相互作用模型初值问题解的全局适定性

本文利用Banach不动点原理对Hirota与Satsuma提出的一类耦合非线性波相互作用模型之初值问题进行了讨论，得到其解在Hs（R）XHs（R），S≥1，中的全局运定性。

微结构固体中的非光滑孤立波

完善微结构固体的自由能形式,使其包含宏观形变和微形变的全部二次项及宏观形变的三次项,并根据Engelbrecht等修正的微结构弹性理论,严格推导出了描述微结构固体中一维纵波传播的一种新模型.对所得模型进行研究,得到了该模型方程的尖峰孤立波解,进而证明了在一定条件下微结构固体中也可以存在尖峰孤立波.这一结论进一步推广了微结构固体中只存在光滑孤立波的已有结论.

Unscented Kalman filter for SINS alignment

In order to improve the filter accuracy for the nonlinear error model of strapdown inertial navigation system （SINS） alignment, Unscented Kalman Filter （UKF） is presented for simulation with stationary base and moving base of SINS alignment. Simulation results show the superior performance of this approach when compared with classical suboptimal techniques such as extended Kalman filter in cases of large initial misalignment. The UKF has good performance in case of small initial misalignment.

Financial Rogue Waves

We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.

Nonpropagating Solitons in （2＋1）-Dimensional Dispersive Long-Water Wave System

With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.

A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea

A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow.One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained.The model simulations describe the generation and propagation of internal waves well.When the strength of imposed barotropic tides and the water stratification stay unchanged,the steepness of the sill slope can control both(a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves,and(b) the amplitude of the internal solitary waves generated.If the steepness of the sill is asymmetric,the nonlinear internal solitary waves may be induced on the steeper side of the sill.These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.

组合KdV方程的齐次平衡法求解

利用齐次平衡方法研究了组合KdV方程ut+auux+ 6u2 ux+uxxx=0的孤波解结构 。

Fully Coupled Time-Domain Simulation of Dynamic Positioning Semi-Submersible Platform Using Dynamic Surface Control

A fully coupled 6-degree-of-freedom nonlinear dynamic model is presented to analyze the dynamic response of a semi-submersible platform which is equipped with the dynamic positioning(DP) system. In the control force design, a dynamic model of reference linear drift frequency in the horizontal plane is introduced. The dynamic surface control(DSC) is used to design a control strategy for the DP. Compared with the traditional back-stepping methods, the dynamic surface control combined with radial basis function(RBF) neural networks(NNs) can avoid differentiating intermediate variables repeatedly in every design step due to the introduction of a first order filter. Low frequency motions obtained from total motions by a low pass filter are chosen to be the inputs for the RBF NNs which are used to approximate the low frequency wave force. Considering the propellers' wear and tear, the effect of filtering frequencies for the control force is discussed. Based on power consumptions and positioning requirements, the NN centers are determined. Moreover, the RBF NNs used to approximate the total wave force are built to monitor the disturbances. With the DP assistance, the results of fully coupled dynamic response simulations are given to illustrate the effectiveness of the proposed control strategy.

An Algorithm for Parameter Identification of UAS from Flight Data

The aim of the present work is to realize an identification algorithm especially devoted to UAS （unmanned aerial systems）. Because UAS employ low cost sensor, very high measurement noise has to be taken into account. Therefore, due to both modelling errors and atmospheric turbulence, noticeable system noise has also to be considered. To cope with both the measurement and system noise, the identification problem addressed in this work is solved by using the FEM （filter error method） approach. A nonlinear mathematical model of the subject aircraft longitudinal dynamics has been tuned up through semi-empirical methods, numerical simulations and ground tests. To take into account model nonlinearities, an EKF （extended Kalman filter） has been implemented to propagate the state. A procedure has been tuned up to determine either aircraft parameters or the process noise. It is noticeable that, because the system noise is treated as unknown parameter, it is possible to identify system affected by noticeable modelling errors. Therefore, the obtained values of process noise covariance matrix can be used to highlight system failure. The obtained results show that the algorithm requires a short computation time to determine aircraft parameter with noticeable precision by using low computation power. The present procedure could be employed to determine the system noise for various mechanical systems, since it is particularly devoted to systems which present dynamics that are difficult to model. Finally, the tuned up off-line EKF should be employed to on-line estimation of either state or unmeasurable inputs like atmospheric turbulence.

Interactions Between Solitons and Cnoidal Periodic Waves of the Boussinesq Equation

The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painleve analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.

Oceanic internal solitary waves in three-layer fluids of great depth

This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth.The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified configuration.Based on the Ablowitz-Fokas-Musslimani formulation for irrotational flows,strongly nonlinear and weakly nonlinear models are developed for the“shallow-shallow-deep”and“deep-shallow-deep”scenarios.Internal solitary waves are computed using numerical iteration schemes,and their global bifurcation diagrams are obtained by a numerical continuation method and compared for different models.For the“shallow-shallow-deep”case,both mode-1 and mode-2 internal solitary waves can be found,and a pulse broad-ening phenomenon resulting in conjugate flows is observed in the mode-2 branch.While in the“deep-shallow-deep”situation,only mode-2 solitary waves can be obtained.The existence and stability of mode-2 internal solitary waves are confirmed by solving the primitive equations based on the MITgcm model.

Predictive control of a direct internal reforming SOFC using a self recurrent wavelet network model

In this paper,an application of a nonlinear predictive controller based on a self recurrent wavelet network (SRWN) model for a direct internal reforming solid oxide fuel cell (DIR-SOFC) is presented. As operating temperature and fuel utilization are two important parameters,the SOFC is identified using an SRWN with inlet fuel flow rate,inlet air flow rate and current as inputs,and temperature and fuel utilization as outputs. To improve the operating performance of the DIR-SOFC and guarantee proper operating conditions,the nonlinear predictive control is implemented using the off-line trained and on-line modified SRWN model,to manipulate the inlet flow rates to keep the temperature and the fuel utilization at desired levels. Simulation results show satisfactory predictive accuracy of the SRWN model,and demonstrate the excellence of the SRWN-based predictive controller for the DIR-SOFC.

Design of GaAs/Al_xGa_(1-x)As asymmetric quantum wells for THz-wave by difference frequency generation

The energy levels, wave functions and the second-order nonlinear susceptibilities are calculated in GaAs/Al0.2Ga0.8As/Al0.5Ga0.5As asymmetric quantum well （AQW） by using an asymmetric model based on the parabolic and non-parabolic band. The influence of non-parabolicity can not be neglected when analyzing the phenomena in narrow quantum wells and in higher lying subband edges in wider wells. The numerical results show that under double resonance （DR） conditions, the second- order difference frequency generation （DFG） and optical rectification （OR） generation susceptibilities in the AQW reach 2.5019 μm/V and 13.208 μm/V, respectively, which are much larger than those of the bulk GaAs. Besides, we calculate the absorption coefficient of AQW and find out the two pump wavelengths correspond to the maximum absorption, so appropriate pump beams must be selected to generate terahertz （THz） radiation by DFG.