Xianxi Dai

Exact and explicit solitary wave solutions to a model equation for water waves

Abstract Exact and explicit solitary wave solutions are obtained for the higher order Korteweg-d Vries equaion, which has been obtained recently in a formal asymptotic approximation for water waves with surface tension.

On a specific heat-phonon spectrum inversion problem. Exact solution, unique existence theorem and Riemann hypothesis

Abstract In this paper a problem and an integral equation, determining the phonon density of states by a measured lattice specific heat, are suggested. Its exact solution formula, unique existence theorem, the technique for eliminating divergence and some exact soluble models are given. The possible relation between the unique existence theorem for the inversion problem in physics and the Riemann hypothesis, which is an unsolved problem in mathematics, is also discussed.

Some solitary wave solutions for families of generalized higher order KdV equations

Abstract In this paper some families of the generalized higher order KdV equation (the [ v ] type and the [ v,v ′] type families) are suggested. The higher order KdV equation, which has been studied recently for water waves with surface tension, is a special case of the families of the generalized higher order KdV equation. In this paper a class of functions G(λ, ξ) is studied and is used to solve these equations. A class of exact solitary wave solutions is obtained.

A new approximation in the functional integral approach: Beyond the first harmonic approximation

Abstract The single cross diagram approximation (SCD), beyond the first harmonic approximation (FHA) in the functional integral approach (FIA), is realized for the first time. The exact relation proved by Xianxi Dai [J. Phys. Condens. Matter 3 (1991) 4389; 4 (1992) 1339] and a complete integral representation of the ψ function turn out to be very useful in the numerical calculation. The numerical results for the symmetric Anderson model show that the SCD is better than the FHA in the medium temperature region for small and medium Coulomb interaction U . The method of cancelling the infinite singularities is universal in the diagram technique in the FIA.

Exact treatments of activation energy, quantum tunneling and flux-creep rate in high-Tc superconductors

Abstract Within the framework of both thermally activated and quantum-tunneling flux-creep models, an exact treatment of the activation energy, the quantum tunneling and the flux-creep rate in high-Tc superconductors is presented. For a typical quartic pinning potential in a various medium, the parameter-dependent activation energy and quantum tunneling of the system are studied in detail. Reliable determinations of the magnetic relaxation rate for a given strong type-II high-Tc superconductor will enable a check of the validity of the theoretical results.

Exact solution of the thermally activated flux-creep model on type-II superconductors

Abstract The model of thermally activated flux creep is reanalyzed theoretically, since the approximate solution of the Anderson-Kim model is inadequate to describe the flux creep in high- T c superconductors. An exact solution of this model is derived. It is shown that this simple phenomenological theory best describes the magnetic relaxation data obtained in both high- T c and low- T c superconductors.

Soliton pairing superconducting string model for high-Tc superconductivity

Abstract We explore a possible mechanism for high- T c superconductivity by a soliton pairing superconducting string model in connection with the main features of copper oxide. We formulate the superconducting condensation energy and investigate the physical origin of soliton pairing due to the doping-induced coupling. We finally discuss several experimental consequences for YBaCuO and LaSrCuO systems.

A set of exact and explicit solitary wave solutions for a class of generalized KdV equations with arbitrary odd order derivatives (a sieving method in a closed function class)

Abstract Recent higher order KdV equations are interesting for physics, for example when the surface tension approaches close to a certain value. In this paper using the method of sieving in a closed function class, a set of exact and explicit solitary wave solutions with a unified form are given to higher order or generalized higher order KdV equations with 7th, 9th or arbitrary odd order derivatives, when their parameters satisfy some suitable restricted conditions.

Theory of the measurement of resistivity of superconductors and its dual integral equations

Abstract The theory of measurement of the anisotropic resistivity for high T c superconductors is studied. A dual integral system of equations is proposed and its decoupling and dimension reduction are performed. The singularity of the integral kernel is removed and its solution and correction curve are presented. The numerical result is applied to make the formula used in resistivity measurements more reasonable and precise.

Tc enhancement in multilayered compounds with interlayer and intralayer couplings

Abstract We show that the dependence of T c on the number of CuO 2 layers in Tl- and Bi-base compounds can be analytically derived based on a model proposed by Ma and Dai taking into account two types of coupling, interlayer and intralayer. We demonstrate that T c is enhanced by the cooperation of the two couplings. Using the observed critical temperature for n = 1, 2 and 3, we calculate the T c of the higher numbers of layers and find them to be in agreement with the experimental trend.