The steady solution and its stability of Nonlinear Schrdinger Equation (NLSE) are studied by means of traveling wave transformation and bifurcation theory.
用行波变换方法和分叉理论研究里非线性薛定谔方程的定常解和定常解的稳定性。
This paper Studies nonlinear wave equation with dissipation items, reaching an approximate solution in the method of parameter differentiation.
对一类带耗散项非线性波动方程进行了研究，用“参数微分法”，得到其解析近似解。
Our results show that the equation has at least one solution provided the nonlinear term satisfies a linear growth restriction.
我们的结论表明如果非线性项满足某种线性增长限制则该方程至少有一个解。
The existence theorem shows that the equation has at least one solution provided the nonlinear term satisfies a linear growth condition.
这个存在定理说明只要非线性项满足某种线性增长条件该方程至少有一个解。
It is very difficult to get analytic solution except some very specific cases for the model owing to nonlinear partial differential equation.
由于非饱和流动的数学模型归结为非线性的偏微分方程，除了一些很特殊的情况外，很难得到解析解。
This paper presents a new iterative formula by which the solution of nonlinear equation had rapid and absolute convergence.
提出了一个新的迭代公式，用此公式求解非线性方程根收敛速度快，且绝对收敛。
This paper studies nonlinear wave equation with dispersion items, reaching an approximate Solution in the method of Parameter differentiation.
对带色散项非线性控制方程进行了研究，用“参数微分法”，得到其近似解。
This paper studies the existence of solution for a semilinear wave equation under the nonlinear term and initial value satisfying certain conditions.
本文研究了半线性波动方程在非线性项和初值满足一定条件下解的存在性。
A high accuracy algorithm for numerical solution of nonlinear partial differential equation (PDE) is suggested combining wavelet collocation method with generalized energy integral.
将小波配置法与广义能量积分相结合，提出了一种求解非线性偏微分方程的高精度数值方法。
The existence of periodic solution to nonlinear functional difference equation is considered by using the topological degree, and a periodic solution of this problem is obtained.
利用拓扑度理论对一类非线性泛函差分方程周期解的存在性进行了讨论，得到该问题周期解的一个存在定理。
By reducing the MREIT problem to a nonlinear operator equation, the formal derivative of the operator and the formula of solution for linearization problem are given.
通过将问题化为非线性算子方程，推导出算子的形式导数，给出了线性化问题解的等价表达。
A method to find real numerical solution of the nonlinear equation by logarithm complex conversion is presented in this paper.
本文提出一种通过对数复变换求非线性方程实数根数值解的方法。
We prove that the solution of a nonlinear complementarity problem is exactly the equilibrium point of differential equation system, and prove the asymptotical stability and global convergence.
在一定的条件下我们证明了非线性互补问题的解是该微分方程系统的平衡点，并且证明了该微分方程系统的稳定性和全局收敛性。
This paper also gives the differential equation of the nonlinear vibration model, and obtains its asymptotic solution by means of singular perturbation methods.
文中给出了这一非线性振动模型的微分方程，并用奇异摄动法求得了渐近解。
The properties of solution to a class of quasilinear degenerate parabolic system coupled via three nonlinear diffusion equation are considered.
研究了由三个拟线性退化抛物型方程通过非线性项耦合而得到的一类拟线性退化抛物方程组解的性质。
The extinction phenomenon of solution is one of the important qualities of nonlinear parabolic partial differential equation, as it explains comprehensive realistic backgrounds.
解的熄灭现象是非线性抛物型方程解的一个重要性质，有着广泛的物理背景。
The exact stationary solution of a class of nonlinear dynamic problems subjected to Gaussian white noise has been obtained by solving its corresponding Fokker Planck Kolmogorov equation.
一类受高斯白噪声激励的非线性动力学方程能通过求解对应的F Pk方程得到精确稳态解。
The solution of the nonlinear wave equation describing propagation of a femtosecond laser pulse with duration of several optical oscillation periods in a nonlinear fiber is presented.
给出了描述具有几个光振荡周期的飞秒激光脉冲在非线性光纤中传输方程的解。
The approximate solution to the nonlinear differential dynamic equation of a swing is derived by using another simple method, which is very suitable for discussing in class.
用另一种方法导出了秋千非线性动力学微分方程的近似解，很适合课堂讨论。
In this paper , the undermined function method has been used to study the analytic solution of nonlinear orbit differential equation. In a case four kinds analytic solution are given.
利用待定函数法研究了非线性轨道微分方程的解析解，求出了一类情形下的四类解析解。
In this paper, a method of asymptotic integral is suggested for determining the periodical solution of a nonlinear equation. Examples are given.
本文提出非线性方程周期解的渐近积分法，并举例说明。
In this paper, we introduce the numerical solution of nonlinear equation with a integration and discuss the convergence of algorithm.
本文提出了一类含积分的非线性方程的数值算法，并讨论了算法的收敛性。
The nonlinear equation of heat conduction is transformed into a Laplace's equation by applying the Kirchhoff transformation, and an analytic approximate solution of the equation is derived.
当介质的导热系数是温度的函数时，热传导方程是非线性偏微分方程，作者采用基尔霍夫变换把它变成拉普拉斯方程，于是可以找到原问题的近似解析解。
The existence of solution and positive solution is considered for a fourth-order nonlinear elastic beam equation with derivatives of all orders.
考察了一类非线性四阶弹性梁方程的解和正解的存在性。
A new approach for solution of nonlinear algebraic and differential equation sets was presented.
提出一种求解非线性代数方程和非线性常微分方程的新方法。
A variable length simple pendulum model is introduced, elementary analysis and perturbation analytic solution of nonlinear differential equation for parametric resonance are presented.
采用可变长度单摆的力学模型对秋千振荡给出初等分析，采用微扰近似法导出了秋千的非线性参数共振解析解， 并进行了讨论。
In chapter 4, for 2d nonlinear convection-dominated diffusion equation, a two-grid scheme of characteristic finite-element solution is constructed.
第四章里，对二维非线性对流扩散方程，构造了特征有限元的两重网格算法，并给出了相应的收敛性分析，数值例子。
The existence of solution and positive solution is considered for a fourth-order nonlinear elastic beam equation with derivatives of all orders.
考察了含有各阶导数的一个4阶非线性弹性梁方程的解和正解的存在性。
The existence of solution and positive solution is considered for a fourth-order nonlinear elastic beam equation with derivatives of all orders.
考察了含有各阶导数的一个4阶非线性弹性梁方程的解和正解的存在性。
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