A simple solitary wave solution and infinitely many rational function solutions, especially the closed form of the solution for the initial value problem of the higher order Broer-Kaup (BK) systems in (1+1) and (2+1) dimensions, are obtained by using the extended homogeneous balance method.

We transform the problem of seeking the planar wave speed in general excitable media into a cubically algbraic equation, thus we can find the explicit representation of the planar wave speed (in one-dimensional case, the traveling wave speed) and dispersive relation. Especially for a few typical excitable media, we give the formula for calculating the corresponding wave speed.

We consider the case that one of entangled atoms interacts with a single-mode cavity field. The atom is selectively detected after exiting the cavity, and it is found that the nonclassical properties of field states depend strongly on the entanglement degree between the two atoms. Meanwhile it is proven that squeezing of field and photon antibunching can be greatly enhanced via selective atomic measurements.

The interaction between soliton and sinusoidal wave in two weakly coupled long Josephson junctions is studied. Theoretical analysis reveals that the soliton may be embedded in Melnikov chaotic attractors and the Fiske-step-modes are implied in the boundedness condition of the system. Comparison between the chaotic soliton oscillators and synchronized soliton oscillators shows that the former possesses greater maximal velocity and energy.

The intensity-dependent nonlinear refraction phenomena in a non-resonant multilevel molecular system is studied using rate equations in steady state, including saturable refraction, reverse saturable refraction, and the turnover between these two effects. The relationship between the refraction saturation and the optical Kerr effect is also discussed.

A five-parameter nonlinear model is introduced to the description of the stretching vibrational modes of benzene molecule in the electronic ground state, and is applied for the first time to the calculations of energy levels of C-H and C-D stretches of C₆H₆ and C₆D₆ in vapor phase. The results obtained agree well with the experimental vibrational energy levels and with the results obtained from other model calculations. Moreover, our model calculations predict accurately some new overtone and combination bands that have not been studied experimentally.

Based on the global analysis of all available and reliable data for isotopic species ¹⁴N^mO(m=16,17,18), the ¹⁴N¹⁶O rovibrational spectral lines are calculated with very high accuracy and completely agree with previous results. These lines with relative intensities can be achieved as an infrared frequency standard in the spectral range 1600-5600 cm^-1. The calculated rovibrational transitions of ¹⁴N^mO(m=17,18) have the same accuracy as that for ¹⁴N¹⁶O although their data are rare due to their small natural abundance.

Using a repulsive vortex-vortex interaction model, we numerically investigate the dynamics of vortices in a driven disordered two-dimensional superconductor. At low driving forces and temperatures, we have seen the evidence of plastic and filamentary flow. At high driving forces and very low temperatures, the evidence of an ordering of the moving vortices is seen in the flux flow regime. Our results are in agreement with the previous simulation results and recent experiments.

By using the fusion method, we give the spin-1 XXX chain associated with sl₂ with two arbitrary spin boundary impurities. Then the exact diagonalized Hamiltonian of this model was obtained by the means of Bethe ansatz method.

With the help of absorption and fluorescence spectra, the spectroscopic properties of Tm³⁺, Ho³⁺:YVO₄ crystals have been investigated under different dopant concentrations. The absorption results show that the maximum absorption in the spectral range of currently available powerful laser diodes (LD) is at 796 nm, corresponding to the transition ³H₆→³H₄ of Tm³⁺ in the crystals. Upon the excitation with a LD at 808 nm, we have detected ten fluorescence bands in the spectral range spanning from visible to infrared. In visible region 4 upconversion bands have been observed centered at 475, 547, 660, and 701 nm. Discussions of the energy transfer processes suggest that cross relaxations and excited absorptions with the involvement of Tm^{3+ 3}F₄, ³H₅ and Ho^{3+ 7}I₅ states are responsible for the four upconversion emissions. Comprising the relative integrated intersities of 2 μm (Ho³⁺: ⁵I₇→⁵I₈) and 1.8 μm (Tm³⁺: ³F_4→³H₆) bands we have observed an efficient energy transfer from Tm³⁺ (³F₄) to Ho³⁺ (⁵I₇). Examination of the ratios of the intensity of 2 μm band to that of 1.8 μm band as a function of the ratios of Tm³⁺ concentration (c_Tm) to Ho³⁺ concentration (c_Ho) indicates that small concentration ratios (c_Tm/c_Ho) lead to high efficient energy transfers of Tm³⁺(³F₄)→Ho³⁺(⁵I₇).

A number of TiNi samples with different compositions and states were measured by positron annihilation technique. And microdefects and the influence of them on shape memory effect were analyzed, giving some valuable information for the study of technological processes of preparing TiNi functional shape memory devices.