New Solutions to Generalized mKdV Equation

Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and more new kinds of solitary wave solutions are obtained.

Applications of Extended Hyperbolic Function Method for Quintic Discrete Nonlinear SchrSdinger Equation

By using the extended hyperbolic function method, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution, bright and dark soliton solution, alternating phase bright soliton solution, alternating phase dark soliton solution, and alternating phase bright and dark soliton solution, if a special relation is bound on the coefficients of the equation.

Extended Complex tanh-Function Method and Exact Solutions to （2＋1）-Dimensional Hirota Equation

In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is more powerful than the complex tanh-function method [Chaos, Solitons and Fractals 20 （2004） 1037]. Abundant new solutions o[ （2q-1）-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.

Analysis to Some Solutions Obtained by Modified Extended tanh-Function Method

First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear evolution equations are given. The results show that when balance number m is one or two, the tanh-eoth type solutions obtained by the modified extended tanh-funetion method can be obtained by using the hyperbolic-function method.

考虑长径比影响的黄土地区钻孔灌注桩桩侧摩阻力取值研究

为研究长径比对黄土地区钻孔灌注桩桩侧摩阻力的影响,采用1/30的相似比设计了3根长径比不同的模型试验桩MS1,MS2,MS3,并对其进行了室内加载试验,通过分析3根试桩的荷载-沉降曲线、桩身轴力和桩侧摩阻力的变化,研究了其承载和沉降特性。基于荷载传递法建立了单桩荷载传递模型,经过理论分析,推导出双曲线函数中参数a的表达式,拟合出参数b的表达式,利用双曲线函数表达式计算出室内试验用土的桩侧摩阻力。结合2个依托工程,利用推导出的双曲线函数法求解了黄土状土、老黄土的桩侧摩阻力,将实测结果和数值模拟结果进行了对比分析。结果表明:(1)当竖向荷载小于极限荷载时,随着长径比的增大,桩顶沉降量减小,当达到极限荷载以后,随着长径比的增大,桩顶沉降量增大;(2)随长径比的增大,桩端阻力占荷载的比例逐渐减小,桩侧摩阻力达到极限值的位移逐渐下移,并且数值减小,桩身上部的侧摩阻力优先充分发挥作用,随后桩身下部的侧摩阻力开始工作,承担荷载;(3)利用双曲线函数计算的桩侧摩阻力与实测结果的误差最小为7.08%,可以满足工程要求,因此双曲线函数解析法可以用于求解工程中桩基的侧摩阻力;(4)利用双曲线函数法求解的2个依托工程的桩侧摩阻力与实测值、模拟值相比误差均在15%以内,说明可将考虑参数修正的双曲线函数法应用于黄土地区桩基桩侧摩阻力标准值的取值计算。