共查询到20条相似文献,搜索用时 119 毫秒
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为了研究非线性发展方程的有界衰减振荡解,特选取Fisher方程为例. Fisher方程在描述激发介质的非数值模型(如Belousov-Zhabotinsky (BZ)反应)中, 其解的振幅取负值是有意义的.应用平面动力系统理论,研究了Fisher方程有界行波解存在的条件, 利用LS解法和线性化解法给出了其有界衰减振荡解的近似解析表达式,并进行了误差估计. 相似文献
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基于虚功原理, 在Hu X Y等和Grenier N等的研究结果基础上推导了多相流光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)控制方程, 采用精度较高的黏性力和表面张力模型, 发展了一套适用于具有大密度比和大黏性比界面的多相流SPH方法. 首先, 通过施加人工位移修正, 适当背景压力和异相界面力, 使得计算全程粒子分布相对均匀, 改善了界面处的失稳现象, 防止了异相界面处粒子的非物理性穿透; 在此基础上, 利用方形流体团振荡模型对表面张力模型进行了验证, 数值结果与解析解甚为吻合; 然后采用上浮气泡经典数值算例对比研究了不同黏性力计算方法、不同核函数的适用性以及人工位移修正的效果; 最后, 对单个气泡的上浮、变形、撕裂以及垂向两个气泡的追赶、融合等现象进行了模拟, 初步揭示了气泡上浮过程中各种有趣物理现象的细节过程和动力学机理. 相似文献
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We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained. 相似文献
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在中国聚变工程实验堆(CFETR)螺旋波的设计参数下,提出一种多阵列行波天线用于螺旋波电流驱动的方案.利用电磁仿真软件CST对三维天线的参考模型进行了仿真,结果表明,在50MHz带宽内,天线电压驻波比<1.2,且天线阵列激发的k谱具有很好的定域性,有利于提高天线的电流驱动效率. 相似文献
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以Barkley模型为研究对象, 研究了在时空调制作用下螺旋波时空动力学行为特性. 发现在适当的调制参数的作用下, 能够在同一系统中同时观察到漫游螺旋波与旅行螺旋波. 通过数值模拟研究分析, 给出了能产生漫游螺旋波与旅行螺旋波共存现象的潜在机理, 并详细讨论了在Barkley 模型中要产生这种共存现象的两个必要条件.
关键词:
时空调制
漫游螺旋波
旅行螺旋波 相似文献
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A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation (CGLE), that describes dissipative semiconductor laser cavity is derived. Using perturbation method, the stability region is identified. Bifurcation analysis is done by smoothly varying the cavity loss coefficient to provide insight of the system dynamics. He’s variational method is adopted to obtain the standard sech-type and the not-so-explored but promising cosh-Gaussian type, travelling wave solutions. For a given set of system parameters, only one sech solution is obtained, whereas several distinct solution points are derived for cosh-Gaussian case. These solutions yield a wide variety of travelling wave profiles, namely Gaussian, near-sech, flat-top and a cosh-Gaussian with variable central dip. A split-step Fourier method and pseudospectral method have been used for direct numerical solution of the CGLE and travelling wave profiles identical to the analytical profiles have been obtained. We also identified the parametric zone that promises an extremely large family of cosh-Gaussian travelling wave solutions with tunable shape. This suggests that the cosh-Gaussian profile is quite generic and would be helpful for further theoretical as well as experimental investigation on pattern formation, pulse dynamics and localization in semiconductor laser cavity. 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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Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential 下载免费PDF全文
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation. 相似文献
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We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding (multi-component) travelling wave solutions under certain physical conditions. A number of physical models (molecular chains, coupled Josephson junctions, propagation of kinks in chains of adsorbed atoms and domain walls) are considered as examples. 相似文献
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This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis. 相似文献