试探方程法及其在非线性发展方程中的应用

提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式，再利用三阶多项式的完 全判别系统求解，由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解 关键词： 试探方程法 非线性发展方程 孤波解 Jacobi椭圆函数 周期解     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

Production of long,laminar plasma jets at atmospheric pressure with multiple cathodes

Plasma jets from conventional non‐transferred arc plasma devices are usually operated in turbulent flows at atmospheric pressure. In this paper, a novel non‐transferred arc plasma device with multiple cathodes is introduced to produce long, laminar plasma jets at atmospheric pressure. A pure helium atmosphere is used to produce a laminar plasma jet with a maximum length of >60 cm. The influence of gas components, arc currents, anode nozzle diameter, and gas flow rate on the jet characteristics is experimentally studied. The results reveal that the length of the plasma jet increases with increasing helium content and arc current but decreases with increasing nozzle diameter. As the gas flow rate increases, the length of the plasma jet initially increases and then decreases. Accordingly, the plasma jet is transformed from a laminar state to a transitional state and finally to a turbulent state. Furthermore, the anode arc root behaviours corresponding to different plasma jet flows are studied. In conclusion, the multiple stationary arc roots that exist on the anode just inside the nozzle entrance are favourable for the generation of a laminar plasma jet in this device.     

On the performance of a virtual user pairing scheme to efficiently utilize the spectrum of unpaired users in NOMA

This paper evaluates the performance of a virtual user pairing scheme that efficiently utilizes the spectrum of unpaired users in non-orthogonal multiple access (NOMA), termed as VP-NOMA. The scheme aims at utilizing the frequency bands of those users which remain unpaired due to the non-uniform distribution of users in a cellular area. We consider a case where the cell edge users are more than the cell center users, so that complete one-to-one correspondence does not exist between all cell center and cell edge users to be accommodated/paired using conventional NOMA (C-NOMA) user pairing. Thus, some cell edge users remain unpaired, and are served using conventional multiple access (OMA) schemes. In such scenario, VP-NOMA pairs a single cell center user with two or more clustered (closely located) cell edge users over non-overlapping frequency bands, thus enabling the cell center user to efficiently use the frequency bands of these previously unpaired cell edge users. Performance of VP-NOMA in terms of ergodic sum capacity (ESC), outage probability (OP), and outage sum capacity (OSC), is analyzed through comprehensive mathematical derivations and simulations for a generalized system model. Moreover, the mathematical analysis is validated through close concordance between analytical and simulation results of ESC, OP, and OSC.     

The Fifth Order Peregrine Breather and Its Eight-Parameter Deformations Solutions of the NLS Equation

We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters. This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.     

Studying effect of MHD on thin films of a micropolar fluid

This paper deals with the study of the effect of MHD on thin films of a micropolar fluid. These thin films are considered for three different geometries, namely: (i) flow down an inclined plane, (ii) flow on a moving belt and (iii) flow down a vertical cylinder. The transformed boundary layer governing equations of a micropolar fluid and the resulting system of coupled non-linear ordinary differential equations are solved numerically by using shooting method. Numerical results were presented for velocity and micro-rotation profiles within the boundary layer for different parameters of the problem including micropolar fluid parameters, magnetic field parameter, etc., which are also discussed numerically and illustrated graphically.     

Motzkin numbers out of Random Domino Automaton

Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.     

Annular billiards with position-dependent mass

We present exact solutions for the position-dependent mass Schrödinger equation (PDMSE) in an annular billiard with impenetrable walls where the mass is allowed to depend on the radial position, i.e., μ=μ(r)$\mu =\mu \left(r\right)$. Exact wavefunctions are calculated explicitly for four mass distributions.     

Symmetry Analysis of Two Types of （2＋1）-Dimensional Nonlinear Klein-Gorden Equation

By means of the classical symmetry method, we investigate two types of the （2＋1）-dimensional nonlinear Klein-Gorden equation. For the wave equation, we give out its symmetry group analysis in detail. For the second type of the （2＋1）-dimensional nonlinear Klein-Gorden equation, an optimal system of its one-dimensional subalgebras is constructed and some corresponding two-dimensional symmetry reductions are obtained.