非线性演化方程的孤立波解

用齐次平衡原则和辅助微分方程方法得到了6个重要的n次非线性演化方程的孤立波解.辅助微分方程方法的主要思想是借助简单的可解微分方程的解去构造复杂的非线性演化方程的行进波解.这里简单的可解微分方程称为辅助微分方程.本文使用的辅助方程有双曲正割幂型解或双曲正切幂型解.     

立方非线性Schr?dinger方程的Jacobi椭圆函数周期解

本文利用F-展开法,求出了立方非线性Schrodinger方程的由Jacobi椭圆函数表示的行波解;并且在极限情况下,得到了方程的孤波解.     

Klein-Gordon-Schrodinger方程组的精确孤立波解

利用齐次平衡原则导出Klein-Gordom-Schrodinger方程组的精确孤立波解.该解在形式上比文献中纯理论的存在性证明的结果更一般,文献中的解的形式是该结果的特殊情形.     

变形浅水波方程组的一个非线性变换及其应用

本文用齐次平衡方法导出了变形浅水波方程组的一个非线性变换,借助该变换得到了方程组的精确孤立波解。     

一变系数非线性发展方程组的自-BT及其精确解

利用齐次平衡原则,导出了一变系数非线性发展方程组的自-Baecklund变换(自-BT);借助此自-BT和变系数热传导方程的各种精确解用代数的方法获得了方程组的各种精确解。     

The periodic wave solutions for two systems of nonlinear wave equations

The periodic wave solutions for the Zakharov system of nonlinear wave equations and a long－short-wave interaction system are obtained by using the F-expansion method, which can be regarded as an overall generalization of Jacobi elliptic function expansion proposed recently. In the limit cases, the solitary wave solutions for the systems are also obtained.     

Exact Solitary Wave Solutions of Nonlinear Evolution Equations with a Positive Fractional Power Term

The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type. In the special cases that the fractional power equals to 1 and 2, the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.     

基于气温指数的我国天气衍生品定价研究

本文以时间序列分析中的ARMA模型和均值回复模型为基础,依据不同的纬度自北向南依次选取了北京、南京、杭州和广州作为合约城市,基于四城市1951-2011年的历史气温数据对各模型参数进行估计,并运用蒙特卡洛模拟定量检验各模型对我国天气衍生品定价的适应性。研究表明:基于日波动率的均值回复模型在预测准确性以及对不同基线温度的适应性方面要优于基于月波动率的均值回复模型和ARMA模型,更适合我国天气衍生品的定价;不同的基线温度对于各模型的预测准确率有较大的影响,因此我国在推出天气衍生品时如果考虑冬夏季月份设置不同的基线温度,那么冬季基线温度不宜过低,夏季基线温度不宜过高。     

EXACT SOLITARY WAVE AND SOLITONSOLUTIONS OF THE FIFTH ORDER MODEL EQUATION

1 Introduction and Mds ResultsMathematical modeling of physical systems Often leads to nonlinear evolution equations.EXat solutions of such equations axe of haPortance in physical problexns, and in Particu1arthere is considerable interest in solitary wave solutiOns and soliton solutions. In this paPer, wepresent tlie solitary wave and sOliton sOlutions Of a fiftli order nonlillear evolution eqllation.Suppose u(x, t) satisfies fOllowing nonlinear 5th-order evolutiOn equation Of the fOrmut…