The （w/g）-expansion method and its application to Vakhnenko equation

This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the (ω/g)-expansion method, which can be thought of as the generalization of (G /G)-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.     

Brick Walls for Nonstationary Black Holes

The validity condition of the brick-wall model is analysed in nonstationary space-time.It is shown that the model holds only in thin regions,only by using tortoise coordinates near the event horizon of a slowly varying(quasistationary)black hole.The reason for the use of tortoise cooridnates is that the stationary state solutions of quantum field equations in other coordinates do not exist for any region in nonstationary space-time.Meanwhile,the quantum corrections to the entropy of the Vaidya-Bonner black hole due to the spin fields are calculated in terms of the brick-wall model.     

A study on the multi-freedom broadband impedance model for time-domain simulations

The purpose of this paper is to construct a general broadband impedance model, which is suited for predicting acoustic propagation problems in time domain.A multi-freedom broadband impedance model for sound propagation over impedance surfaces is proposed and the corresponding time domain impedance boundary condition is presented.Basing on the extended Helmholtz resonator,the multi-freedom impedance model is constructed through combing with a sum of rational functions in the form of general complex-conjugate pole-residue pairs and it is proved that the impedance model is well posed.The impedance boundary condition can be implemented into a computational aeroacoustics solver by a recursive convolution technique, which results in a fast and computationally efficient algorithm.The two dimensional and three dimensional benchmark problems are selected to validate the accuracy of the proposed impedance model and time domain simulations.The numerical results are in good agreement with the reference solutions.It is demonstrated that the proposed impedance model can be used to describe the broadband characteristics of acoustic liners,and the corresponding time domain impedance boundary condition is viable and accurate for the prediction of sound propagation over broadband impedance surfaces.     

A New Method for Constructing Travelling Wave Solutions to the modified Benjamin--Bona--Mahoney Equation

We present a new method to find the exact travelling wave solutions of nonlinear evolution equations, with the aid of the symbolic computation. Based on this method, we successfully solve the modified BenjaminBona-Mahoney equation, and obtain some new solutions which can be expressed by trigonometric functions and hyperbolic functions, It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.     

Soliton solution and interaction property for a coupled modified Korteweg-de Vries （mKdV） system

Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.     

New structures for closed-form wave solutions for the dynamical equations model related to the ion sound and Langmuir waves

This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves.The modified(G'/G)-expansion procedure is utilized to raise new closed-form wave solutions.Those solutions are investigated through hyperbolic,trigonometric and rational function.The graphical design makes the dynamics of the equations noticeable.It provides the mathematical foundation in diverse sectors of underwater acoustics,electromagnetic wave propagation,design of specific optoelectronic devices and physics quantum mechanics.Herein,we concluded that the studied approach is advanced,meaningful and significant in implementing many solutions of several nonlinear partial differential equations occurring in applied sciences.     

Investigation of combined Brillouin gain and loss in a birefringent fiber with applications in sensing

The most general model of elliptical birefringence in an optical fiber is extended to describe a transient Bril-louin interaction including both gain and loss. The effects of elliptical birefringence cause a Brillouin spectral shape distortion, which is detrimental for fiber sensing techniques. The model investigates the effects of bire- fringence and the corresponding evolution of spectral distortion effects along the fiber, and also investigates regimes where this distortion is minimal.     

New Agegraphic Dark Energy in Brans-Dicke Theory

In this paper, we investigate the new agegraphic dark energy model in the framework of Brans-Dicke theory, which is a natural extension of the Einstein＇s general relativity. In this framework the form of the new agegraphic dark energy density takes as pq = 3n^2Ф（t）η^-2, where η is the conformal age of the universe and Ф（t） is the Brans-Dicke scalar field representing the inverse of the time-variable Newton＇s constant. We derive the equation of state of the new agegraphic dark energy and the deceleration parameter of the universe in the Brans-Dicke theory. It is very interesting to find that in the Brans-Dicke theory the agegraphic dark energy realizes quintom-like behavior, i.e., its equation of state crosses the phantom divide ω= -1 during the evolution. We also compare the situation of the agegraphic dark energy model in the Brans-Dicke theory with that in the Einstein＇s theory. In addition, we discuss the new agegraphic dark energy model with interaction in the framework of the Brans-Dicke theory.     

Generalized and Improved （G＇/G）-Expansion Method Combined with Jacobi Elliptic Equation

In this article, we propose an alternative approach of the generalized and improved （G＇/G）-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti- Leon-Pempinelle equation, the Pochhammer-Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacob/elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations.     

Numerical solution of a stationary nonisothermal two-phase filtration problem by the steadying method

The structure of solutions of a stationary nonisothermal problem of the two-phase filtration of immiscible fluids is studied numerically. The character of the convergence of nonstationary solutions to stationary ones is investigated. It is shown that at different parameter values the solution may have an interval, where s(x) ≡ 0 or s(x) ≡ 1. The temperature effect on the structure of the solutions of the equation for water saturation is investigated. The work was partially supported by the SB RAS (Integration Project No. 117).     

非线性演化方程椭圆函数解的一种简单求法及其应用

非线性演化方程的许多行波解可以写成满足投影Riccati方程的两个基本函数的多项式形式.利用这一性质，通过建立一般的椭圆方程与投影Riccati方程解之间的关系，导出了一个构造这些解的新方法.该方法对类型Ⅰ的方程和类型Ⅱ的方程均有效，同时也回答了如何求出非线性演化方程分式形式椭圆函数解的问题. 关键词： 非线性演化方程 椭圆函数解     

New Modified Jacobi Elliptic Function Expansion Method and Its Application to (3+1)-Dimensional KP Equation

With the aid of computerized symbolic computation, the new modified Jacobi elliptic function expansion method for constructing exact periodic solutions of nonlinear mathematical physics equation is presented by a new general ansatz. The proposed method is more powerful than most of the existing methods. By use of the method, we not only can successfully recover the previously known formal solutions but also can construct new and more general formal solutions for some nonlinear evolution equations. We choose the (3+1)-dimensional Kadomtsev-Petviashvili equation to illustrate our method. As a result, twenty families of periodic solutions are obtained. Of course, more solitary wave solutions, shock wave solutions or triangular function formal solutions can be obtained at their limit condition.     

New periodic wave solutions via Exp-function method

The Exp-function method with the aid of symbolic computational system is used to obtain the generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics, namely, nonlinear partial differential (BBMB) equation, generalized RLW equation and generalized shallow water wave equation. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics.     

Extended Riccati Equation Rational Expansion Method and Its Application to Nonlinear Stochastic Evolution Equations

In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.     

A Unified Explicit Construction of 2N-Soliton Solutions for Evolution Equations Determined by 2×2 AKNS System

An explicit N-fold Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed. By using the Darboux transformation, the solutions of the evolution equations are reduced to solving alinear algebraic system, from which a unified and explicit formulation of 2N-soliton solutions for the evolution equation are given. Furthermore, a reduction technique for MKdV equation is presented, and an N-fold Darboux transformation of MKdV hierarchy is constructed through the reduction technique. A Maple package which can entirely automatically output the exact N-soliton solutions of the MKdV equation is developed.     

双曲函数型辅助方程构造具5次强非线性项的波方程的新精确孤波解

在辅助方程法的基础上利用两种函数变换和一种双曲函数型辅助方程，通过符号计算系统Mathematica构造了在力学当中一个重要的模型，有5次强非线性项的波方程的新三角函数型和双曲函数型精确孤波解.这种方法寻找其他具5次强非线性项的非线性发展方程的新精确解方面具有普遍意义. 关键词： 双曲函数型辅助方程 函数变换 具5次强非线性项的波方程 精确孤波解     

Heisenberg Model in a Rotating Magnetic Field

We study the Heisenberg model under the influence of a rotating magnetic field. By using a time-dependent unitary transformation, the time evolution operator for the Schrödinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are calculated, and are expressed in terms of the solid angle subtended by the closed trace of the total spin vector, as well as in terms of those of the individual spins.     

A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony （mBBM） model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.