The strong symmetry of the general KdV equation is factorized to a simple form and then the inverse strong symmetry is obtained explicitly. Acting a strong symmetry of the general KdV equation on the trivial symmetry and the known re symmetry, we obtain four new sets of symmetries of the general KdV equation. All these sets of symmetries constitute an infinite dimensional Lie algebra.

A matrix method is presented for treating the dynamical phases, adiabatic phases and nonadiabatic phases of quantum superposition states. It is effective for any parameter-varying Hamiltonian system. As two examples, the evolution of mass-varying harmonic oscillator and the evolution of coherent states under parameter-varying displaced operator have been studied, Some new phenomena are obtained in the first case and the possible producing of so-called Schr?dinger's cat state by geometric phases is pointed out. The quantum state useful for the quantum optical verification of Berry's phase is introduced.

The coupled wave equations and their analytic solutions in photorefractive crystals are presented for the case of two-beam writing, while the light-induced scattering is considered, Using this result, the diffraction efficiency for each writing beam is discussed in doped KNSBN crystals with unidirectional fan, which is explained theoretically and verified exper-imentally.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

This paper presents a perturbation model for calculating the approximate Lamb wave velocities in solid adhesive joints. The numerical computations show that the approximate values of the Lamb wave velocities are very close to the exact ones if the thickness of the interface layer is small. A comparison of the perturbation analysis with the approximate "spring" model is given. The significance of the perturbation model is discussed for the inverse deduction of the mechanical properties of the interface layer from Lamb wave measurements.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

A double-well resonant tunneling structure has been investigated carefully using the nonequilibrium Green's function method. We find that in the transmission probability two maxima appear even when the two levels have the same energy. This characteristic is at-tributed to the resonant tunneliug through mixed quasibound states. The tunneling current formula through this system under a dc voltage has been derived exactly. Three different cases are considered and several novel properties are found, which manifest coherent charac-teristics of the tunneling process.

The dependence of critical current density J_{c} on the angle α between the directions of the applied magnetic field H (which was rotated in the c-axis-I plane) and the in-plane current I was measured on a c-axis oriented epitaxial YBa_{2}Cu_{3}O_{7-δ} films at 81 K, with the magnetic field strength up to 6T. Analysis of the experimental results on the basis of the classical scaling law of pinning force shows that there exist simultaneously planar-pinning and volume-pinning mechanisms, and the contribution of volume pinning increases wish decreasing while that of the planar pinning decreases, We propose that the decrease of Lorentz-force-independent critical current density with increasing H for H∥I results from the suppression of superconductivity by the magnetic field, The fact that the contribution of volume pinning increases with decreasing α also arises from the suppression of superconductivity in CuO_{2} plane by the magnetic field.

We have investigated, by X-ray diffraction, a series of single crystals of Bi-based oxides with the nominal composition Bi_{2}Sr_{2}(Cu_{1-z}Fe_{z})O_{6+δ}(0≤z≤0.55). In this system we observed two structural phase transitions with the increase of the doping content. The first transition, from an incommensurate monoclinic phase to an incommensurate orthorhombic phase, occurs at a doping content of iron z_{Fe}=0.027. The second one corresponds to a phase transition from an incommensurate orthorhombic phase to a commensurate orthorhombic phase at z_{Fe}=0.34. The comparison of these results with those for more limited substitutions of Zn and Ni indicates the significant role of the insertion of the extra oxygen in the (Bi-O)_{∞} double layers.

Dy_{2}Fe_{17-x}Ga_{x} (x = 0,1,2,3,4, 5 and 6) compounds were prepared by arc melting. These compounds are of single phase, having a hexagonal Th_{2}Ni_{17}-type structure fox x=0 and rhombohedral Th_{2}Zn_{17}-type structure for x≥1. The substitution of Ga for Fe in the Dy_{2}Fe_{17} leads to a linear increase of unit-cell volumes. The saturation magnetization M_{s} at 1.5K is found to decrease linearly with increasing Ga concentration, from 65emu/g for x= 0 to 5emu/g for x = 6; and the Fe magnetic moment μ_{Fe} is almost independent of Ga concentration. The Curie temperature T_{C} is found first to increase with increasing Ga content x, and goes through a maximum value of 559 K at about x = 3, then decreases. The sharp increase of T_{C} at lower Ga content may result from the increase of unit cell volumes. Dy_{2}Fe_{17-x}Ga_{x} compounds with x≤5 exhibit easy plane anisotropy at room temperature, and those with x = 6 possess easy-axis.

On the basis of the "exercise" experiment and the phenomenon of "self-shrink", the behavior of "less-stable" IDs (first kind of dumbbell domains) in radial contraction under an "exercise" bias field, (H_{b})_{e}, was statistically investigated in detail. It was found that the histograms of their stripe-to-bubble transition field, H_{sb} after exercise, become narrower and shift towards the side of lower H_{sb} with the increase of (H_{b})_{e}. It illustrates how the less-stable IDs lose part of their vertical Bloch lines under different (H_{b})_{e}. In addition, it was also found that the curve of the upper boundary of these histograms, (H_{sb})_{max} vs. (H_{b})_{e}, consists of two segments of straight lines. This discontinuity was proved to be due to self shrink, and the crosspoint of these two lines is just the lower limit of the self-shrink region. Furthermore, a series of photographs were taken to show the effect of radial contraction on less-stable IDs intuitively.

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