New Peakons and Periodic Peakons of the Modified Camassa-Holm Equation

In this paper, we obtain new peakon and periodic peakon solutions to a modified Camassa-Holm equation. We change the modified Camassa- Holm equation into a planar system. Then the first integral and algebraic curves of this system are obtained. By using the first integral and algebraic curves, a new peakon solution is given by hyperbolic function. Moreover, some new periodic peakons are given by elliptic functions and triangle functions.     

周期性管柱信道的声波通信技术研究综述

井下声波通信技术利用周期性管柱信道实时传输声波数据，相比于其他通信方式，具有适应性好、复杂度低、传输效率高等优点，在随钻地质导向、油水井监测等方面有广阔的应用前景，是发展智能油田的关键技术之一。本文主要综述上世纪90年代以来关于信道物理模型、信道容量、声信号调制与接收方法等关键问题的研究历程，并对通信系统的设计要点与国内外相关产品的现场应用进行梳理，为后续的技术改进提供依据。     

Periodic Solutions of the Duffing Differential Equation Revisited via the Averaging Theory

We use three different results of the averaging theory of first order for studying the existence of new periodic solutions in the two Duffing differential equations $\ddot y+ a \sin y= b \sin t$ and $\ddot y+a y-c y^3=b\sin t$, where $a$, $b$ and $c$ are real parameters.     

A perfectly matched layer for finite-element calculations of diffraction by metallic surface-relief gratings

We introduce a perfectly matched layer approach for finite element calculations of diffraction by metallic surface-relief gratings. We use a non-integrable absorbing function which allows us to use thin absorbing layers, which reduces the computational time when simulating this type of structure. In addition, we numerically determine the best choice of the absorbing layer parameters and show that they are independent of the wavelength.     

Periodic,breather and rogue wave solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Periodic wave solutions are constructed by virtue of the Hirota–Riemann method. Based on the extended homoclinic test approach, breather and rogue wave solutions are obtained. Moreover, through the symbolic computation, the relationship between the one-periodic wave solutions and one-soliton solutions has been analytically discussed, and it is shown that the one-periodic wave solutions approach the one-soliton solutions when the amplitude $\eta \to 0$.