Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities

Conservation laws for a class of variable coefficient nonlinear wave equations with power nonlinearities are investigated.The usual equivalence group and the generalized extended one including transformations which are nonlocal with respect to arbitrary elements are introduced.Then,using the most direct method,we carry out a classification of local conservation laws with characteristics of zero order for the equation under consideration up to equivalence relations generated by the generalized extended equivalence group.The equivalence with respect to this group and the correct choice of gauge coefficients of the equations play the major roles for simple and clear formulation of the final results.     

Symmetry solutions of a nonlinear elastic wave equation with third-order anharmonic corrections

Lie symmetry method is applied to analyze a nonlinear elastic wave equation for longitudinal deformations with third-order anharmonic corrections to the elastic energy. Symmetry algebra is found and reductions to second-order ordinary differential equations （ODEs） are obtained through invariance under different symmetries. The reduced ODEs are further analyzed to obtain several exact solutions in an explicit form. It was observed in the literature that anharmonic corrections generally lead to solutions with time-dependent singularities in finite times singularities, we also obtain solutions which Along with solutions with time-dependent do not exhibit time-dependent singularities.     

Finite Symmetry Transformation Groups and Exact Solutions of Lax Integrable Systems

The general Lie point symmetry groups of the Nizhnik-Novikov-Vesselov （NNV） equation and the asymmetric NNV equation are given by a simple direct method with help of their weak Lax pairs.     

AuCu3熔体快速冷却过程中的键对与多面体

Based on the FS(Finnis-Sinclair) many-body potential model, the rapid cooling process of a system, which consists of 375 Cu atoms and 125 Au atoms, controlled by period boundary condition was simulated. The dependence of pair distribution function of melten compound AuCu3 on the temperature under these conditions was researched. It can be concluded that the noncrystal exists under 700 K, and the liquid-glass transition temperature is approximately 680 K according to the Abraham′s method. Furthermore, the feature of version of cluster in melten AuCu3 was investigated by Honeycutt pair analysis technique. It is demonstrated that the structural configuration in melten AuCu3 has remarkable variation during the formation of noncrystal according to the relationship between the bonded pairs and polyhedron and temperatures. The defective polyhedra in liquid AuCu3 have greatest changes accompanying the changing temperatures.     

Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models. Received 8 February 2000 and Received in final form 25 April 2000     

The different effect of electron-electron interaction on the spectrum of atoms and quantum dots

Though atoms and quantum dots typically contain a comparable number of electrons, the number of discrete levels resolved in spectroscopy experiments is very different for the two systems. In atoms, hundreds of levels are observed while in quantum dots that number is usually smaller than 10. In the present work, this difference is traced to the different confining potentials in these systems. In atoms, the soft confining potential leads to large spatial extent of the excited electron's wave function and hence to weak Coulomb interaction with the rest of the atomic electrons. The resulting level broadening is smaller than the single particle level spacing and decreases as the excitation energy is increased. In quantum dots, on the other hand, the sharp confining potential results in electron-electron scattering rates that grow rapidly with energy and fairly quickly exceed the approximately constant single particle level spacing. The number of discrete levels in quantum dots is hence limited by electron-electron interaction, whose effect is negligible in atoms. Received 3 April 2000 and Received in final form 7 August 2000     

Aharonov-Bohm effect in one-channel weakly disordered rings

A new diagrammatic method, which is a reformulation of Berezinskii's technique, is constructed to study the density of electronic states of a one-channel weakly disordered ring, threaded by an external magnetic flux. The exact result obtained for the density of states shows an oscillation of with a period of the flux quantum . As the sample length (or the impurity concentration) is reduced, a transition takes place from the weak localization regime () to the ballistic one (). The analytical expression for the density of states shows the exact dependence of on the ring's circumference and on disorder strength for both regimes. Received 27 December 1999     

Symmetries and conservation laws of one Blaszak–Marciniak four-field lattice equation

In this paper, by using the classical Lie symmetry approach, Lie point symmetries and reductions of one Blaszak– Marciniak(BM) four-field lattice equation are obtained. Two kinds of exact solutions of a rational form and an exponential form are given. Moreover, we show that the equation has a sequence of generalized symmetries and conservation laws of polynomial form, which further confirms the integrability of the BM system.