厄尔尼诺/拉尼娜-南方涛动机制时滞海-气振子的渐近解

研究了一类厄尔尼诺/拉尼娜-南方涛动机制. 利用渐近分析的摄动方法,简单而有效地构造了一个厄尔尼诺/拉尼娜和南方涛动时滞模型解的渐近展开式. 讨论了相应问题解的渐近性态. 关键词： 非线性 渐近性态 厄尔尼诺/拉尼娜-南方涛动模型     

一类厄尔尼诺海-气时滞振子的渐近解

研究了一类厄尔尼诺-南方涛动机制. 利用奇异摄动理论和方法求出了厄尔尼诺-南方涛动模型的外部解及初始层校正项. 从而得到问题解的渐近展开式, 并讨论了解的渐近性态. 关键词： 非线性 渐近解 厄尔尼诺-南方涛动模型     

ENSO非线性模型的摄动解

研究了一类ENSO摄动模型.利用摄动理论和方法，构造了相应问题的渐近展开式. 关键词： 非线性 摄动 ENSO模型     

厄尔尼诺-南方涛动时滞海-气振子耦合模型

研究了一个时滞海-气振子模型.利用摄动理论和方法，得到了海-气振子模型解的渐近展开式. 关键词： 非线性 时滞 厄尔尼诺-南方涛动 海-气振子     

一类厄尔尼诺海-气振子机理的摄动解

研究了一类厄尔尼诺-南方海涛(ENSO)机理耦合系统振荡.利用摄动理论和方法，较简便地得到了一类ENSO模型解的一致有效的渐近展开式. 关键词： 非线性 摄动理论 厄尔尼诺-南方涛动模型     

具有控制项的弱非线性发展方程行波解

利用解析方法研究了一类具有控制项的弱非线性发展方程. 由摄动理论得到了相应方程的渐近解,并研究了控制项对渐近解的影响. 关键词： 发展方程 扰动 控制函数     

一类奇摄动薄板弯曲问题的匹配渐近解

研究了一类薄板弯曲问题. 对四阶奇摄动边值问题, 引入伸长变量, 构造边界附近的内层解, 然后与外部解匹配. 最后用合成展开式理论, 得到了原问题的的渐近解. 关键词： 薄板弯曲 挠度 渐近解     

双参数奇摄动非线性反应扩散问题

讨论了一类具有双参数的非线性反应扩散方程奇摄动初始边值问题.在适当的假设下,构造了解的渐近展开式并讨论了它的渐近性态.     

边界耦合的Marangoni对流边界层问题的近似解析解

研究了由温度梯度引起的Marangoni对流边界层问题.由于动量方程和能量方程的边界条件耦合,利用相似变换将偏微分方程组转化为常微分方程非线性边界值问题.通过巧妙引入摄动小参数对速度和温度边界层方程同时渐近展开求解,得到了问题的近似解析解,并对相应的动量、能量传递特性进行了讨论. 关键词： Marangoni对流 近似解析解 渐近展开     

一类厄尔尼诺时滞海-气振子摄动解

研究了一类厄尔尼诺-南方涛动(ENSO)的时滞振子耦合系统. 利用时滞理论, 摄动等方法求出了ENSO模型解的渐近式,并讨论了相应问题的渐近性态. 关键词： 非线性 摄动 ENSO模型     

Asymptotic solution for a perturbed mechanism of western boundary undercurrents in the Pacific

This paper consider a class of perturbed mechanism for the western boundary undercurrents in the Pacific. The model of generalized governing equations is studied. Using the perturbation method, it constructs the asymptotic solution of the model. And the accuracy of asymptotic solution is proved by the theory of differential inequalities. Thus the uniformly valid asymptotic expansions of the solution are obtained.     

Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Nino-Southern Oscillation

A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.     

HIGH-FREQUENCY ASYMPTOTICS FOR THE HELMHOLTZ EQUATION IN A HALF-PLANE

Base on the integral representations of the solution being derived via Fokas' transform method, the high-frequency asymptotics for the solution of the Helmholtz equation, in a half-plane and subject to the Neumann condition is discussed. For the case of piecewise constant boundary data, full asymptotic expansions of the solution are obtained by using Watson's lemma and the method of steepest descents for definite integrals.     

A simple model for radiation damping

Increasing interest has been shown in the method of matched asymptotic expansions for the construction and solution of the equations of motion in general relativity. This paper discusses a simple model which can, in principle, be solved exactly. A comparison of the two solutions shows that the matched asymptotic expansion technique determines correctly the final damping rate and frequency (at least to fourth order in a small parameter), but the phase information is spurious.     

广义Boussinesq方程的同伦映射近似解

研究了一个广义非线性Boussinesq方程. 利用同伦映射方法,首先构造了相应的同伦变换;其次选取了适当的初始近似;然后用同伦映射方法得到了孤立子波近似解;最后得到了微扰渐近表示式. 关键词： Boussinesq方程 非线性 孤立子 近似方法     

Quasi-geometrical optics methods in the theory of wave propagation through a randomly inhomogeneous layer

Some possibilities of using asymptotic methods, such as the Maslov method and the interference-integral method, in problems of wave propagation in randomly inhomogeneous media are considered. It is shown that using the Maslov method and the interference-integral method in a small-angle approximation, and neglecting amplitude fluctuations of partial waves, provides results of heuristic spectral methods that utilize expansions in terms of incoming or outgoing waves. The combined use of these asymptotic methods gives a third heuristic method, a mixed-integral representation obtained earlier by applying the method of two-scale expansions. It is pointed out that results of a mixed-integral representation change to those of the method of smooth disturbances and of the phase-screen method. Unlike the method of two-scale expansions, the proposed approach based on the combined use of asymptotic methods facilitates the process of taking into account the heterogeneity of a background medium.     

Cosmology without singularity and nonlinear gravitational Lagrangians

We investigate the generalized Einstein equations derived from the Lagrangian which is an arbitrary function ofR. The importance of the saturation phenomenon is underlined, which may replace the role of a cosmological constant. The spherically symmetric homogeneous model is analyzed in more detail, and an approximate solution without singularity is constructed using the method of matched asymptotic expansions.     

Disturbed solution of the El Ni?no-southern oscillation sea–air delayed oscillator

A class of delayed oscillators of El Ni?o-southern oscillation (ENSO) models is considered. Using the delayed theory, the perturbed theory and other methods, the asymptotic expansions of the solutions for ENSO models are obtained and the asymptotic behaviour of solution of corresponding problem is studied.