No abstract

Multi-soliton solutions to the modified nonlinear Schrödinger equation (MNLSE) with variable coefficients (VCs) in inhomogeneous fibers are obtained with the help of mapping transformation, which reduces the VC MNLSE into a constant-coefficient MNLSE. Based on the analytical solutions, one- and two-soliton transmissions in the proper dispersion management systems are discussed. The sustainment of solitons and the disappearance of breathers for the VC MNLSE are first reported here.

By means of an extended projective approach, a new type of variable separation excitation with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Based on the derived variable separation excitation, abundant localized coherent structures such as single-valued localized excitations, multiple-valued localized excitations and complex wave excitations are revealed by prescribing appropriate functions. - PACS numbers: 03.65.Ge, 05.45.Yv

No abstract

For studying the vibration characteristics of a laminar composite rotating blade, the spin softening effect calculated by the finite element method (FEM) was incorporated with the prestress effect to analyze shaking, swing, torsion, and coupled vibrations. The mathematical formula was derived. The study shows that the centrifugal force exerts influence on the difference in vibration frequencies. The laminar composite can reduce an influence of the spin softening on the first swing vibration frequency because of its structure and smaller density. With the variation of rotating velocity, the blade spin softening can lead to the coupled first shaking and first swing vibrations. In the coupled vibrations, swing is contained in the shaking mode and shaking is also contained in the swing one, which is the reason of major blade damages. The results confirm the complexity of the dynamic characteristics of the laminar composite rotating blade. This method is also well applicable to the dynamic design of such blades.

We construct four types of analytical soliton solutions for the higher-order nonlinear Schrödinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly. We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons.

No abstract

In order to find the cause of the cracked intermediate axis in a transmission,the characteristic of the bending vibration，torsional vibration and bending-torsional coupling vibration were studied through the analysis of the nature frequency and modal shape based on prestress.The results show that the fatigue fracture of the axis is mainly due to the resonant torsional frequency and bending-torsional coupling vibration and It is basically demonstrated by experiment.It has been found that the fundamental frequency is increase with the increase in spin axis velocity because of the centrifugal load i.e.prestress.The effets can be accounted for by an adjustment of the stiffness,and the dynamic equations are derived.In the end,it is made the optimized design on the axis,the low inherent frequencies are optimized in order to avoid resonance.The problem of the cracked intermediate axis has been solved.