共查询到20条相似文献,搜索用时 159 毫秒
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提出了在微分方程以问题的数值解法中可由一种反问题补充条件时同时反求两个未条参数的观点和方法。并以一维波动方程为例推导了震源和岩性联合反演的详细算法。从概念上突破了传统的一种补充条件只能解一个未知数的反演理论的约束,解决了地震勘探中波动方程反问题的震源未知工测不准的矛盾,缩短了反演理论研究与工程实际应用的间的距离。 相似文献
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随机过程动态自适应小波独立网格多尺度模拟 总被引:1,自引:0,他引:1
在随机过程数值仿真中,由多项式混沌展开谱方法得到求解展开系数的确定性偶合方程组。该方程组比相应的确定性仿真时增大许多。并且当多项式展开阶数和随机空间维数提高时,方程维数急剧增加。由于待求未知分量为表征不同尺度波动的混沌展开模,形成节点意义下的的多尺度问题,传统的网格细分自适应逼近不再适用。为此我们采用了小波的多尺度离散,并建立基于空间细化的动态自适应系统,让每个求解点上的多个未知分量有各自独立的小波网格。本文以随机对流扩散方程为例,进行了二个算例的数值实验,论证了此方法的优点。 相似文献
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裂缝检测是目前国内外石油勘探界研究的一个热点问题,如何确定裂缝方位等参数是石油公司面临的难题,而解决该难题就要确定裂缝方位等参数与地震波场传播之间的定量关系.但是目前所采用的裂缝性地层介质模型不能完全定量地反映裂缝的方位特征和衰减特征.针对该问题,建立了具有任意裂缝方位的裂缝性地层介质模型;并构造了时间增量的方法,将非线性的卷积积分采用近似的方法实现,建立了以位移场表示的具有任意方位角的黏弹性方位各向异性介质的波动方程.该波动方程定量地给出了黏弹性波场特征与裂缝走向的关系,描述了黏弹性地震波在这种介质中的
关键词:
裂缝
各向异性
黏弹性
波动方程 相似文献
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用达朗贝尔公式求解二,三维波动方程的初值问题 总被引:1,自引:0,他引:1
阐述了采用叠加原理,将某些二,三维波方程的初值问题化为一维波动方程的初值问题,进而用达朗贝尔公式对其进行求解的方法。采用这种方法,使这些二三维波动方程初值问题的求解大为简化。 相似文献
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给出横向各向同性介质中SH波的标量波动方程,并通过简单的坐标变换,将其化为标准的Helmholtz方程.建立了求解散射问题的积分方程,利用边界单元方法数值计算了横向各向同性固体中圆柱状空洞及刚性散射体对SH波的散射场分布。重点分析了各向异性对空洞散射体散射场指向性的影响. 相似文献
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Some previously obtained physical solutions [1–3] of Yang’s equations forSU(2) gauge fields [4], Charap’s equations for pion dynamics [5,6] and their combination as proposed by Chakraborty and Chanda
[1] have been presented. They represent different physical characteristics, e.g. spreading wave with solitary profile which
tends to zero as time tends to infinity, spreading wave packets, solitary wave with oscillatory profile, localised wave with
solitary profile which becomes plane wave periodically, and, wave packets which are oscillatory in nature. 相似文献
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This paper deals with small-amplitude waves, described by Maxwell's equations and single-fluid hydrodynamics, in horizontally stratified, continuously varying plasmas with anisotropic electron pressure perturbations. A set of coupled wave equations in first-order matrix form, which describes two different types of obliquely propagating horizontally polarized transverse waves, is treated by the method of Clemmow and Heading. It is then transformed by Heading's method into a form which is valid throughout reflection regions, and from which a pair of second-order coupled wave equation in Fösterling's form follows. 相似文献
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Many oscillatory biological systems show periodic travelling waves. These are often modelled using coupled reaction-diffusion equations. However, the effects of different movement rates (diffusion coefficients) of the interacting components on the predictions of these equations are largely unknown. Here we investigate the ways in which varying the diffusion coefficients in such equations alters the wave speed, time period, wavelength, amplitude and stability of periodic wave solutions. We focus on two sets of kinetics that are commonly used in ecological applications: lambda-omega equations, which are the normal form of an oscillatory coupled reaction-diffusion system close to a supercritical Hopf bifurcation, and a standard predator-prey model. Our results show that changing the ratio of the diffusion coefficients can significantly alter the shape of the one-parameter family of periodic travelling wave solutions. The position of the boundary between stable and unstable waves also depends on the ratio of the diffusion coefficients: in all cases, stability changes through an Eckhaus (‘sideband’) instability. These effects are always symmetrical in the two diffusion coefficients for the lambda-omega equations, but are asymmetric in the predator-prey equations, especially when the limit cycle of the kinetics is of large amplitude. In particular, there are two separate regions of stable waves in the travelling wave family for some parameter values in the predator-prey scenario. Our results also show the existence of a one-parameter family of travelling waves, but not necessarily a Hopf bifurcation, for all values of the diffusion coefficients. Simulations of the full partial differential equations reveals that varying the ratio of the diffusion coefficients can significantly change the properties of periodic travelling waves that arise from particular wave generation mechanisms, and our analysis of the travelling wave families assists in the understanding of these effects. 相似文献
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Han-Xiang Xu Zhan-Ying Yang Li-Chen Zhao Liang Duan Wen-Li Yang 《Physics letters. A》2018,382(26):1738-1744
We study breathers and solitons on different backgrounds in optical fiber system, which is governed by generalized coupled Hirota equations with four wave mixing effect. On plane wave background, a transformation between different types of solitons is discovered. Then, on periodic wave background, we find breather-like nonlinear localized waves of which formation mechanism are related to the energy conversion between two components. The energy conversion results from four wave mixing. Furthermore, we prove that this energy conversion is controlled by amplitude and period of backgrounds. Finally, solitons on periodic wave background are also exhibited. These results would enrich our knowledge of nonlinear localized waves' excitation in coupled system with four wave mixing effect. 相似文献
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光折变介质的相位共轭波强度的近似表达式 总被引:1,自引:0,他引:1
以光折变介质中非线性耦合波微分方程的一种精确解为基础,对在推导这种精确解过程中起重要作用的一个守恒量进行讨论,通过初等变换,在不同的特殊条件下得到相位共轭波强度的几处近似表达式。与报道的其它近似方法相比,本近似方法不需要建立及求解简化的微分方程因而具有普适,简单的特点。 相似文献
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Rayleigh type surface wave propagation in the irregular bottom of ocean model which is the interface of homogeneous liquid layer over laying an irregular boundary of homogeneous orthotropic half space under initial stresses has been discussed in this paper. Three different dispersion equations are obtained in the form of simple equation using and not using Perturbation technique. Some special cases have been considered. The effect of irregularity, initial stressed, point source, and depth of liquid layer on the propagation of Rayleigh waves has been analyzed and results of numerical discussion have been presented graphically for three different dispersion equations. Mainly the graphs are shown the variation of phase velocity with wave number in different cases. 相似文献
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柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象. 相似文献
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By using dynamical system method, this paper considers the (2+1)-dimensional Davey–Stewartson-type equations. The analytical parametric representations of solitary wave solutions, periodic wave solutions as well as unbounded wave solutions are obtained under different parameter conditions. A few diagrams corresponding to certain solutions illustrate some dynamical properties of the equations. 相似文献