We give an introduction to a new direct computational method for constructing multiple soliton solutions to nonlinear equations with variable coefficients in the Kadomtsev–Petviashvili (KP) hierarchy. We discuss in detail how this works for a generalized (3 + 1)-dimensional KP equation with variable coefficients. Explicit soliton, multiple soliton and singular multiple soliton solutions of the equation are obtained under certain constraints on the coefficient functions. Furthermore, the characteristic-line method is applied to discuss the solitonic propagation and collision under the effect of variable coefficients.

We present a scheme for the teleportation of two-qubit entangled atomic states using the idea of a quantum controlled-NOT gate, based on cavity-assisted collisions proposed by Zheng and Guo (2000 Phys. Rev. Lett. 85 2392). In this scheme, there is only virtual exchange of photons; thus the quantum information is not transferred between the atoms and the cavity field and so the decoherence time of the cavity is greatly enhanced.

This paper is concerned with the problem of robust stabilization and H _∞ control for a class of uncertain stochastic neural networks with time-varying delays and time-varying norm-bounded parameter uncertainties. The delay is of a time-varying nature, and the activation functions are assumed to be neither differentiable nor strictly monotonic. Moreover, the description of the activation functions is more general than the commonly used Lipschitz conditions. By using the Lyapunov function approach together with the linear matrix inequality (LMI) technique, for the robust stabilization we propose a state feedback controller to ensure that the closed loop system is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. For the robust H _∞ control problem, a state feedback controller is designed such that in addition to the requirement of robust stability, a prescribed H _∞ performance level is to ...

This paper considers two types of nonlinear partial differential equations, namely the Kaup–Kupershmidt-type (KK-type) equations (KK-I and KK-II), which are of fifth order in space. We propose a Korteweg–de Vries (KdV)-type hierarchy relation and the associated differential operators to show that the KK-type equation can be regarded as a generalization of the KdV-type equation. We also demonstrate the canonical structures for both equations such as the Hamiltonian system, Poisson structure as well as the Ablowitz–Kaup–Newell–Segur structure. The Lax formulations for the KK-type equations are also presented.

Odd-mass iodine nuclei with Z = 53 have low-lying Δ J = 1 and Δ J = 2 bands based on πg _9/2 and πh _11/2 orbitals. Using the particle-rotor model we have investigated the band structure of these states. In this model, the experimental excitation energies of the A + 1 core were fed directly as the input parameter. A standard axially symmetric Nilsson potential has been used with prolate deformation. The parameters of the model were chosen from earlier theoretical work and experimental odd–even mass difference. Only the Coriolis attenuation factor has been treated as the adjustable parameter. We have also investigated the alignment plot to study the alignments of these bands up to fairly high spin. The extracted B( M1)/ B( E2) ratios for the band based on πg _9/2 orbital have been utilized to obtain information about the deformation parameter. With the same deformation parameter exce...

The dynamics of ns →  n′s excitations of hydrogen by positron impact with exponential cosine-screened Coulomb potentials (ECSCPs) has been investigated using a distorted-wave theory in momentum space. Making use of a simple variationally determined wave function for the hydrogen atom, it has been possible to obtain the distorted-wave scattering amplitude in a closed analytical form. A detailed study has been made on differential and total cross sections in the energy range 20–250 eV. To the best of our knowledge, such a study on the differential and total cross sections for inelastic positron–hydrogen collisions with ECSCPs is the first reported in the literature.

We present a study of some mechanical and thermo-physical properties of kesterite-type Cu ₂ZnSnSe ₄ compounds by means of density functional theory-based calculation. The elastic constants of kesterite-type Cu ₂ZnSnSe ₄ have been calculated. The bonding strength along the [100] and [010] directions is the same as that along the [001] direction and the shear elastic properties of the (001) plane are anisotropic for kesterite-type Cu ₂ZnSnSe ₄. The high B/ G ratio shows that the kesterite-type Cu ₂ZnSnSe ₄ compound is prone to ductile behavior. Using the Debye model, relationships among volumes, heat capacity, thermal expansion coefficients, entropy, vibrational energy, internal energy, Gibbs energy and temperature at various pressures have also been predicted in this work. The present results are useful for the design of novel materials based on the kesterite-type Cu ₂ZnSnSe _...

Coherent and incoherent scattering cross sections have been measured using a high purity germanium detector on elements in the range of Z = 13–50 using ²⁴¹Am gamma rays. The cross sections have been derived by comparing the net count rate obtained from the Compton peak of aluminum with the elastic/Compton peak of the target element. The measured cross sections for the coherent and incoherent processes are in agreement with the theoretical values.

A scheme for optical bistability (OB) is proposed, in which the atom is in a four-level tripod configuration and driven by a single elliptically polarized light. It is demonstrated that the behaviors of OB can be controlled efficiently by adjusting the system parameters appropriately. Moreover, phase-controlled OB can be realized as well.

In this paper, we have proposed a model for simple and graded index (GRIN) separate confinement heterostructure (SCH)-based In _0.71Ga _0.21Al _0.08As/InP single-quantum-well lasing heterostructures and studied the energy band structure along with conduction and valence band envelope functions and band offsets. Under theoretical simulation, we have determined the behavior of quasi-Fermi levels in both the conduction and valence bands. Moreover, we have also calculated various important lasing characteristics and the optical gain of the lasing structure as a function of lasing wavelength in transverse electric (TE) and transverse magnetic (TM) modes. For both types of lasing structures, optical gain in the TE mode has been reported to be larger than that in the TM mode. In the TE mode the maximum optical gain for simple and GRIN structures has been achieved at lasing wavelengths of 1.55 and 1.38 μm, respectively, while in the TM mode the values of maximu...