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1.
李红霞 《中国海洋大学学报(自然科学版)》2014,44(11):118-124
本文研究一类具有非对称项和有界扰动项的Duffing方程,推广了王新平在文献[9]中的结论。当扰动项带有时间周期系数时,分别考虑ω为有理数和无理数的情况,对扰动项作出合理的假设后,利用典则变换和Moser小扭转定理的变形,证明了方程的所有解是有界的,即Lagrange稳定性。 相似文献
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讨论一类推广的具竞争扩散Lotka—Volterra系统，利用微分不等式，证明了该系统概周期解的存在唯一性及其在壳扰动下的稳定性；推广和改进了秦发金、罗桂烈等在Lotka—Volterra系统概周期解的结果。 相似文献
3.
本文讨论二点张紧系泊系统,在波流作用下,作平面耦合运动时的非线性响应特性。计算结果显示：由于系泊几何非线性的存在,使得系统存在多个分叉到拟周期解的窗口。 相似文献
4.
热带东风中经向扰动与纬向扰动的非线性相互作用 总被引：1，自引：0，他引：1
根据非线性的动量方程,利用多时间尺度分析方法,探讨由经向扰动与纬向扰动相互作用在热带东风中所造成的一类正压不稳定。分析表明:在零级近似下,给出了两个扰动传播的频率表达式,在一级近似下,得到了两个零级扰动振幅的解析表达式。鉴于方程中散度项的存在,当不同尺度的三个波相作用而发生共振时,仅总动能守恒,而总位拟能不守恒,这一点与无辐散大气的结论不同。两种扰动动能相互转换的机制则是涡度场与散度场的相互作用。 相似文献
5.
本文讨论垂直的中和浮力系留素在浮体的纵向激励处于谐振的情形下的共振响应问题,其中应力应变关系为非线性的。为此,需求解一个在给定边界条件下的非线性方程。利用奇摄动方法可以得到响应的拟周期解。这个解通过共振区后产生分叉。对各个分叉解,我们讨论了它的稳定性。本文方法可推广到亚谐振等情形的处理。 相似文献
6.
作者讨论矩阵方程 ATX+ XTA=B。该方程在 Hamilton力学研究中有用。首先利用L yapunov方程证明了极小 Frobenius范数解的存在性和惟一性。然后用奇异值分解给出了求解最小范数解的一种方法。最后讨论极小范数解的向前扰动分析和最佳向后扰动分析 相似文献
7.
讨论了一类含脉冲的S-分布时滞随机区间细胞神经网络的周期解和指数稳定性问题。利用随机分析的知识、不等式技巧和Poincaré压缩映像理论,研究了系统周期解的存在性和稳定性,得到了S-分布时滞随机细胞神经网络周期解的存在性和全局p阶指数稳定性的新代数判据,同时对周期解的指数收敛率进行了估计,最后通过例子说明了结果的实用性和有效性。 相似文献
8.
研究在外界持续干扰的动态特征已知的情况下,线性离散时滞系统的前馈-反馈最优控制问题。给出了前馈-反馈最优控制存在的唯一性条件,提出了前馈-反馈最优控制律的逐次逼近算法;通过截取最优控制序列解的有限项,得到系统的前馈-反馈次优控制律,并利用扰动观测器解决了其物理可实现问题。该算法容易实现,计算工作量小,且对外部持续扰动有良好的鲁棒性。仿真结果说明了算法的有效性。 相似文献
9.
利用运动学模型 ,研究了弯曲急流控制参数为定常和发生周期扰动时的流体质点运动轨迹以及混沌现象的产生机制。发现弯曲急流控制参数为定常时 ,流体质点的运动为规则的周期运动 ;而控制参数发生扰动时 ,可以发生流体质点在不同特征区的穿行 ,流体质点的运动具有混沌特性。弯曲急流的相速、振幅发生周期扰动均可使流体质点的运动出现混沌特性。作者从运动学上对弯曲急流区的漂流浮标混沌特性给出了解释。 相似文献
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本文研究在圆环区域上带梯度项和完全非线性项的半线性椭圆型方程边值问题径向大解的爆破速率。在证明一些重要极限的基础上,与常微分方程分析法相结合得到了当完全非线性项满足Keller-Osserman条件,梯度项的指数范围分别在0～1和大于2时径向大解的爆破速率及在加强的条件下大解边界行为的第二次影响. 相似文献
12.
本文研究了1类具梯度项的次线性椭圆型方程大解和完全有界解的存在性问题。运用上下解方法和极值原理分别得到了Rn上方程存在完全大解的充分必要条件和存在完全有界解的充分条件,并且证明了该方程在Rn中光滑有界区域Ω上不存在大解。 相似文献
13.
Solutions of the eikonal equation and the first two transport equations are derived for problems involving ray chaos. The solution of the eikonal equation approximates the phase. The solutions of the transport equations approximate the amplitude as an asymptotic series in ω-1. Examples are presented to illustrate that the second term in the series grows relative to the first term along some rags. This secular behavior is associated with the exponential decay of amplitude, which occurs along chaotic rays. The results suggest that chaotic ray solutions (including ray paths, phases, and amplitudes) break down rapidly with range. Although the analysis is limited to a special case that is free of caustics, the results bring into question the use of chaotic ray solutions for long-range propagation 相似文献
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本文研究带梯度项的半线性椭圆型方程正径向整大解的存在性.先利用Banach不动点定理和反证法得出正径向解的局部及整体存在性,进而得到正径向整大解的存在性结论.结果发现,正径向整大解的存在性依赖于梯度项的系数符号和指数的范围. 相似文献
15.
Hong-Sheng Zhang Hong-Jun Zhao Ping-Xing Ding Guo-Ping Miao 《Ocean Engineering》2007,34(10):1393-1404
By transforming two different time-dependent hyperbolic mild slope equations with dissipation term for wave propagation on non-uniform currents into wave-action conservation equation and eikonal equation, respectively, shown are the different effects of dissipation term on the eikonal equation in the two different mild slope equations. The performances of intrinsic frequency and wave number are also discussed. Thus the suitable mathematical model is chosen in which the wave number vector and intrinsic frequency are expressed both more rigorously and completely. By using the perturbation method, an extended evolution equation, which is of time-dependent parabolic type, is developed from the time-dependent hyperbolic mild slope equation which exists in the suitable mathematical model, and solved by using the alternating direction implicit (ADI) method. Presented is the numerical model for wave propagation and transformation on non-uniform currents in water of slowly varying topography. From the comparisons of the numerical solutions with the theoretical solutions of two examples of wave propagation, respectively, the results show that the numerical solutions are in good agreement with the exact ones. Calculating the interactions between incident wave and current on a sloping beach [Arthur, R.S., 1950. Refraction of shallow water waves. The combined effects of currents and underwater topography. EOS Transactions, August 31, 549–552], the differences of wave number vector between refraction and combined refraction–diffraction of waves are discussed quantitatively, while the effects of different methods of calculating wave number vector on numerical results are shown. 相似文献
16.
By means of the classical method, we investigate the (3+1)-dimensional Zakharov--Kuznetsov equation. The symmetry group of the (3+1)-dimensional Zakharov--Kuznetsov equation is studied first and the theorem of group invariant solutions is constructed. Then using the associated vector fields of the obtained symmetry, we give the one-, two-, and three-parameter optimal systems of group-invariant solutions. Based on the optimal system, we derive the reductions and some new solutions of the (3+1)-dimensional Zakharov--Kuznetsov equation. 相似文献
17.
Deriving analytical solutions for tide-induced groundwater fluctuations in unconfined aquifers confronts two problems: (1) As the Boussinesq equation itself contains nonlinear terms, the "secular term" would be generated in derivation, thus making perturbation solution unable to be deduced to higher order; (2) for aquifers with sloping beaches, the perturbation parameter in existing analytical solution integrating the beach slope and hydrogeological property would be sometimes larger than 1. So the application of perturbation solutions is relatively limited. Furthermore, as the beach slope decreases, the error of analytical solution would gradually increase. Given that water table over-height would increase the aquifer thickness and speed up wave propagation, this paper integrates over-height into the perturbation parameter and adjusts boundary conditions to settle the problem of "secular term" and to derive a new high-order analytical solution for nonlinear Boussinesq equation in terms of sloping beaches. Results show that the new analytical solution is more reasonable, and the analytical accuracy is obviously improved in comparison with the existing analytical solution for a gentle slope. The new analytical solution provides a theoretical basis for analyzing the propagation characteristics (e.g., wave length and over-height variation) of tide-induced groundwater wave in unconfined aquifers, particularly those with sloping beaches. 相似文献
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Hidekazu Yasuda 《Journal of Oceanography》2004,60(3):587-596
The fundamental nature of the mass flux due to the shear effect is examined analytically in a basin with steady and oscillatory
currents to promote a better understanding of the mass transport process in coastal waters. The currents are given from solutions
of the simplified motion equation so as to be consistent with the diffusion equation. The matter concentration used is given
by an analytical solution of the diffusion equation with the settling flux term contained. Mass flux, yielding the depth-averaged
dispersion coefficient, is rather varied vertically in both steady and oscillatory currents. In the oscillatory current with
a Stokes layer in particular, the vertical profile of flux is more complicated and even negative flux is induced near the
basin floor. This negative flux does not necessarily yield a negative value of the vertically averaged dispersion coefficient.
The exact dispersion coefficient given by the flux analysis is realized only in the steady state of the matter concentration
distribution, though we can scarcely observe the steady state in the actual sea. The vertically uniform longitudinal dispersion
coefficient at the stationary stage is shown to be caused from the vertical complexity of mass flux by the action of the vertical
diffusing and the settling flux.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
李红 《中国海洋大学学报(自然科学版)》1995,(4)
研究一类二阶非线性差分方程解的振动性质，并且得到了保证方程一切解振动的某些新的充分条件。尤其是，在本文取得的结果中，还包括并推广了最近张炳根、庚建设和王志成在国外杂志上发表的某些研究结果。 相似文献