NONLINEAR WATER WAVE PROPAGATING OVER UNEVEN BOTTOMS

Various types of wave group solutions of the weakly nonlinear waves may exist over uneven bottoms. In this paper, the variation of the zeroes of the dispersive and nonlinear terms,and the wave group solution in the third-order evolution equations are described for the case of mild and locally fastvarying water depths.

Alienor Method for Nonlinear Multi-Objective Optimization

This paper deals with the Alienor method to tackle multiobjective nonlinear optimization problems. In this approach, the multiple criteria of the optimization problem are aggregated into a single one using weighted sums. Then, the resulting single objective nonlinear optimization problem is solved using the Alienor method associated with the Optimization Preserving Operators technique which has proved to be suitable for (nonlinear) optimization problems with a large number of variables (see [1]). The proposed approach is evaluated through test problems. The results show that the approach provides good approximations of the Pareto front while requiring small computational time, even for large instances.

Recent advances in nonlinear optics for bio‐imaging applications

Nonlinear optics,which is a subject for studying the interaction between intense light and materials,has great impact on various research fields.Since many structures in biological tissues exhibit strong nonlinear optical effects,nonlinear optics has been widely applied in biomedical studies.Especially in the aspect of bio-imaging,nonlinear optical techniques can provide rapid,label-free and chemically specific imaging of biological samples,which enable the investigation of biological processes and analysis of samples beyond other microscopy techniques.In this review,we focus on the introduction of nonlinear optical processes and their applications in bio-imaging as well as the recent advances in this filed.Our perspective of this field is also presented.

Exact Solutions to Nonlinear Schr(?)dinger Equation and Higher-Order Nonlinear Schr(?)dinger Equation

We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.

ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

This paper studies the ioteraction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged domain. By using the method of constructing asymptotic solutions and Newton’s iteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will be given in the following paper.

Synthesis and Characterization of a Series of New Functional Poly(ferrocenylenesilanes) for Nonlinear Optics

A series of new poly(ferrocenylenesilanes) containing carbazole as charge transporting agent and Dispersed Red 1 (DR-1) as second-order nonlinear optical (NLO) chromophore was synthesized. The resulting polymers represent the first example of NLO polymer with ferrocenyl groups in the backbone. This series of polymers was characterized with H-1 NMR, UV-vis, IR spectroscopies, differential scanning calorimeter (DSC) and gel permeation chromatography (GPC). A preliminary measurement on NLO property of the polymers was carried out with in-situ second-harmonic generation (SHG) measurement.