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High-quality superconducting Ca1−x Na x Fe2As2 single crystals have been successfully grown by the NaAs-flux method, with sodium doping level x = 0.4–0.64. The typical sizes of these crystals are more than 10 mm in ab-plane and ∼ 0.1 mm along c-axis in thickness. X-ray diffraction, resistance and magnetization measurements are carried out to characterize the quality of these crystals. While no signature of magnetic phase transitions is detected in the normal state, bulk superconductivity is found for these samples, with a sharp transition at T c ranging from 19.8 K (x = 0.4) to 34.8 K (x = 0.64). The doping dependences of the c-axis parameter and T c are consistent with previous reports, suggesting a possible connection between the lattice parameters and superconductivity.

A nonlinear Schroodinger equation in one-dimensional bead chain is first obtained and an envelope solitary wave of the system is verified numerically in this system. The reflection and the transmission of an incident envelope solitary wave due to impurities has also been investigated. It is found that the magnitudes of both the reflection and the transmission not only depend on the characters of impurity materials, the wave number, the incident wave amplitude, but also on the impurity number. This can be used to detect the character and the number of the impurity materials in the bead chain by measuring the reflection and the transmission of an incident pulse.

By means of the multiple-scale expansion method, the coupled nonlinear Schrodinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose–Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.

We study the Landau?Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.

A one-dimensional (1D) Frenkel–Kontorova (FK) model is studied numerically in this paper, and two new analytical solutions (a supersonic kink and a nonlinear periodic wave) of the Sine–Gordon (SG) equation (continuum limit approximation of the FK model) are obtained by using the Jacobi elliptic function expansion method. Taking these new solutions as initial conditions for the FK model, we numerically find there exist the supersonic kink and the nonlinear periodic wave in these systems and obtain a lot of interesting and significant results. Moreover, we also investigate the subsonic kink and the breather in these systems and obtain some new feature.

This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincare–Lighthill–Kuo perturbation method, it obtains two Korteweg–de Vries equations for nonlinear waves in both the ξ and η directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of u(υ) up to O(e3) order is given.

This paper presents the mono-vacancy formation and migration energies of each element Ti, Ga, and C in the MAX phase Ti2GaC, which are obtained by first principles calculations. We also calculate the formation energies of oxygen substituting for Ti, Ga, and C and two formation energies of oxygen interstitial in different sites. The results show that the formation energy of oxygen substituting for Ti is the highest, and the formation energies of the O substitution for Ga atoms decrease as the oxygen concentration increases. The two different formation energies of one oxygen interstitial show that the stable site for the oxygen interstitial is at the center of the triangle composed by three Ga atoms. The effects of vacancy, oxygen substitution, and the interstitial on the electronic properties of Ti2GaC are also discussed in light of the density of states and the electron charge density.

We investigate the tunneling dynamics of the Fermi gases in an optical lattice in the Bose–Einstein condensation (BEC) regime. The three critical scattering lengths and the system energies are found in different cases of Josephson oscillation (JO), oscillating-phase-type self-trapping (OPTST), running-phase-type self-trapping (RPTST), and self-trapping (ST). It is found that the s-wave scattering lengths have a crucial role on the tunneling dynamics. By adjusting the scattering length in the adiabatic condition, the transition probability changes with the adiabatic periodicity and a rectangular periodic pattern emerges. The periodicity of the rectangular wave depends on the system parameters such as the periodicity of the adjustable parameter, the s-wave scattering length.

By employing the quantum hydrodynamic model for electron—ion—dust plasma, we derive a dispersion relation of the quantum dusty plasma. The effects of the dust size distribution on the dispersion relation in a cold quantum dusty plasma are studied. Both analytical and numerical results are given to compare the differences between the dusty plasma by considering the dust size distribution and the mono-sized dusty plasma. It is shown that many system parameters can significantly influence the dispersion relation of the quantum dusty plasma.

This paper investigates the collision between two nonlinear waves with different propagation directions in two-dimensional dust crystals. Using the extended Poincare—Lighthill-Kuo perturbation method, two Korteweg—de Vries equations for nonlinear waves in both the ξ and η directions are obtained, respectively, and the analytical phase shifts and trajectories after the collision of two nonlinear waves are derived. Finally, the effects of parameters of the lattice constant a, the arbitrary constant u0η, the forces f(r), and the colliding angle θ on the phase shifts of both colliding nonlinear waves are examined.

In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the (3+1)-dimensional Kadomtsev—Petviashvili (KP) equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.