Conditional Stability of Solitary-Wave Solutions for Generalized Compound KdV Equation and Generalized Compound KdV-Burgers Equation

In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.

New Travelling Wave Solutions to Compound KdV-Burgers Equation

The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.

Lienard Equation and Exact Solutions for Some Soliton-Producing NonlinearEquations

In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.

Sub-ODE's New Solutions and Their Applications to Two Nonlinear Partial Differential Equations with Higher-Order Nonlinear Terms

In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F12 = AF2 ＋ BF2＋p ＋ CF2＋2p （where F1= dF/dε, p 〉 0） are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 （2007） 115] and IS. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 （2008） 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematics.

New Complexiton Solutions for the(2+1)-dimensional Burgers Equation

In this paper, a new generalized compound Riccati equations rational expansion method （GCRERE） is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method is not only recover some known solutions, but also find some new and general complexiton solutions. Being concise and straightforward, it is applied to the （2＋1）-dimensional Burgers equation. As a result, eight families of new exact analytical solutions for this equation are found. The method can also be applied to other nonlinear partial differential equations.

New Solutions for an Elliptic Equation Method and Its Applications in Nonlinear Evolution Equations

In this paper, we study an elliptic equation with four distinct real roots and obtain five new solutions to this type of elliptic equation. Using these obtained new elliptic function solutions we can construct a series of explicit exact solutions for many nonlinear evolution equations. As examples, we choose combined KdV-MKdV equation, a fourth-order integrable nonlinear Schrödinger equation and generalized Dullin-Gottwald-Holm equation to demonstrate the effectiveness of these new elliptic function solutions. These new elliptic function solutions can be applied to many other nonlinear evolution equations.

Solitons and Other Solutions for the Generalized KdV-mKdV Equation with Higher-order Nonlinear Terms

The generalized sub-ODE method, the rational （G＇/G）-expansion method, the exp-function method and the sine-cosine method are applied for constructing many traveling wave solutions of nonlinear partial differential equations （PDEs）. Some illustrative equations are investigated by these methods and many hyperbolic, trigonometric and rational function solutions are found. We apply these methods to obtain the exact solutions for the generalized KdV-mKdV （GKdV-mKdV） equation with higherorder nonlinear terms. The obtained results confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics. We compare between the results yielding from these methods. Also, a comparison between our new results in this paper and the well-known results are given.

页岩气产量递减规律研究

页岩气藏的渗透率极低,储层流体流动性较差,气井产能较低,其产量递减规律有别于常规气藏。研究页岩气产量递减规律,对预测气田未来产量变化与最终开发指标及指导开发措施调整等均有重要意义。以美国德克萨斯州Haynesville与Barnett页岩气田单井生产动态为例,研究了层状硅质-钙质页岩与层状硅质页岩两大类页岩气田的产量递减规律,分析了复合递减模型以及广义双曲型曲线用于页岩气研究时参数发生的变化及其影响因素。通过Arps广义双曲递减法与复合递减模型法应用的对比表明,层状硅质-钙质页岩与层状硅质页岩两大类页岩气田产量变化规律有较大差异。

广义组合KdV方程与广义组合KdV-Burgers方程孤波解的条件稳定性

讨论了广义组合KdV方程和广义组合KdV Burgers方程的孤波解,在Liapunov意义下的条件稳定性.证明了当行波形式的微小扰动满足一定条件时,这两类方程的精确孤波解具有线性稳定性.

广义解析函数的RDR-HDH复合边值问题

研究了一阶线性椭圆型偏微分方程组的边界条件中含有斜微商的ＲＤＲＨＤＨ复合边值问题．对此，首先把它化为等价的广义解析向量的Ｈｉｌｂｅｒｔ边值问题，然后使用奇异积分方程组的理论。

广义解析函数的RD^2 H复合边值问题(英文)

研究了一阶线性椭圆型偏微分方程的边界条件中含有二阶微商的RD2 H复合边值问题 ,利用消去法将其化为等价的广义解析向量的Hilbert边值问题 。

广义组合KdV方程的线性隐式差分格式

目的研究广义组合KdV方程的数值解.方法利用解KdV方程的方法进行讨论.结果给出了广义组合KdV方程的一种线性隐式差分格式.结论这种线性隐式差分格式是无条件稳定的。

组合KdV型方程孤立波的轨道稳定性

研究了组合KdV型方程ut+aupux+bu2pux+uxxx=0(b≥0,p>0)孤波解的轨道稳定性.研究表明,组合KdV型方程孤波解的轨道稳定性不仅受最高次数非线性项bu2pux的影响,还受到另一非线性项aupux的影响.当b>0,0<p≤2时,该方程恒正的孤波解u1(x-ct)在a>0时轨道稳定,a<0时轨道不稳定;该方程恒负的孤波解u2(x-ct)在a<0时轨道稳定,a>0时轨道不稳定.指出了p=2,a>0时组合KdV型方程的孤波解具轨道稳定性的原因是方程中含系数a的这项具有促使稳定化的作用.

一种广义的(G′/G)-展开法及其应用(英文)

提出了一种广义的(G′/G)-展开法,利用该方法可以得到非线性发展方程的更多不同种类的精确行波解.利用广义的(G′/G)-展开法得到了耦合KdV方程和广义KdV-mKdV组合方程的行波解.

一阶线性椭圆型偏微分方程组的R-H-DH-D^2H复合边值问题

研究了一阶线性椭圆型偏微分方程组的边界条件中含有二阶偏导数的R-H-DH-D2H复合边值问题,利用消去法将该问题化为等价的广义解析向量的Hilbert边值问题,并利用奇异积分方程组理论给出了问题的可解性条件.

两类新的Abel型微分方程的可积判据

借助变量替换法、交换变量位置法及复合函数求导法则,构造出两类新的Abel型微分方程,论证它们的可积性,提供可积的判据,从而推广有关文献的结论,扩大微分方程的可积范围．

广义解析函数的HDH复合边值问题

研究了一阶线性椭圆型偏微分方程组的边界条件中含有斜微商的ＨＤＨ复合边值问题，把它化为等价的广义解析向量的Ｈｉｌｂｅｒｔ边值问题，并给出了可解性条件。

两险种广义复合Poisson模型资金下降到初始盈余的贴现罚金函数

考虑两险种广义复合Poisson模型,研究当资金下降到初始盈余时关于停时的贴现罚金函数.利用概率论方法及Laplace变换,推导出该模型贴现罚金函数满足的积分微分方程以及更新方程,进一步得出贴现罚金函数的具体表达式和资金下降到初始盈余时停时的矩,并对索赔额服从指数分布的情况给出了贴现罚金函数的显式表达式.

广义修正Boussinesq方程孤波解的条件稳定性

讨论了修正Boussinesq方程的钟状孤波解在Liapunov意义下的条件稳定性,证明了当行波形式的微小扰动满足一定条件时,上述方程的孤波解具有线性稳定性.

推广的变系数Caudrey-Dodd-Gibbon方程的精确解

基于Bell多项式法,得到推广的变系数Caudrey-Dodd-Gibbon(CDG)方程的双线性形式。首先,利用摄动方法获得该方程的多孤子解;其次,应用试探函数法并借助数学计算软件Mathematica,得到该方程的双曲函数、三角函数与指数函数的复合型解、Lump解和双曲函数解间的相互作用解;最后,利用已求得的精确解图形说明其性质。