共查询到19条相似文献,搜索用时 31 毫秒
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在正压流体中,利用摄动方法从描写既有Coriolis参数的垂直分量又含有水平分量的位涡方程出发,推导了近赤道非线性Rossby波振幅演变所满足的非线性mKdV方程,并利用Jacobi椭圆函数展开法,求解了推广后的非线性mKdV方程的行波解及孤立波解.通过分析其方程的行波解及孤立波,表明地球旋转的水平分量对Rossby波动产生一定的影响. 相似文献
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本文研究一类强阻尼非线性波方程.通过交换的方法,我们构造了方程的近似惯性流形序列,并得到了对于方程的整体吸引子的逼近估计. 相似文献
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在正压流体中,从包含完整Coriolis参数的准地转位涡方程出发,在弱非线性长波近似下,采用多时空尺度和摄动方法,推导出大气非线性Rossby波振幅演变满足带有外源强迫的二维Zakharov-Kuznetsov(ZK)方程.然后利用Jacobi椭圆函数展开法,求解了ZK方程的椭圆正弦波解和孤立波解.分析结果表明,Coriolis参数的水平分量将影响二维Rossby波传播的频率特征,而外源不仅对二维Rossby波动的传播的频率有影响,对振幅也产生一个调制作用. 相似文献
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《数学物理学报(A辑)》2018,(5)
在正压流体中,从含有完整Coriolis力的准地转位涡方程出发,采用摄动展开的方法推导了,一类新的高阶非线性Schr?dinger方程,用于描述地球流体力学中的非线性调制Rossby波.从方程中,讨论了调制波列.结果表明,完整Coriolis力下的水平分量和地形会影响均匀Rossby波调制不稳定,并且不稳定.区域也会随着改变.此外,均匀基本流也是影响Rossby孤立波调制不稳定性的的重要因素. 相似文献
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三阶非线性KdV方程的交替分段显-隐差分格式 总被引:1,自引:0,他引:1
对三阶非线性KdV方程给出了一组非对称的差分公式,用这些差分公式与显、隐差分公式组合,构造了一类具有本性并行的交替分段显-隐格式A·D2证明了格式的线性绝对稳定性.对1个孤立波解、2个孤立波解的情况分别进行了数值试验.数值结果显示,交替分段显-隐格式稳定,有较高的精确度. 相似文献
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非线性波方程准确孤立波解的符号计算 总被引:75,自引:0,他引:75
该文将机械化数学方法应用于偏微分方程领域,建立了构造一类非线性发展方程孤立波解的一种统一算法,并在计算机数学系统上加以实现,推导出了一批非线性发展方程的精确孤立波解.算法的基本原理是利用非线性发展方程孤立波解的局部性特点,将孤立波表示为双曲正切函数的多项式.从而将非线性发展方程(组)的求解问题转化为非线性代数方程组的求解问题.利用吴文俊消元法在计算机代数系统上求解非线性代数方程组,最终获得非线性发展方程(组)的准确孤立波解. 相似文献
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针对Marion-Temam型非线性Galerkin方法可行性强烈依赖于最小解题规模的不足,利用时滞惯性流形的新思想,以二维Navier-Stokes方程为例,给出了该类非线性Galerkin方法的一种改进形式,并证明了改进后的方法在保持原方法优越性的同时,其可行性条件得到了很大的改善,从而,给出的是一种可行的高效稳定算法。 相似文献
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Yan-Chow Ma 《Studies in Applied Mathematics》1984,70(3):201-213
The evolution equation for the nonlinear Kelvin-Helmholtz wave envelope with its carrier wavenumber near direct resonance is formulated directly by using the nonlinear dispersion relation. The stability of a wavetrain is examined, and the long-time evolution for an arbitrary initial condition is studied through inverse scattering transforms. 相似文献
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A theoretical study is made of the free-surface flow induced by a wavemaker, performing torsional oscillations about a vertical axis, in a shallow rectangular channel near a cut-off frequency. Exactly at cut-off, linearized water-wave theory predicts a temporally unbounded response due to a resonance phenomenon. It is shown, through a perturbation analysis using characteristic variables, that the nonlinear response is governed by a forced Kadomtsev—Petviashvili (KP) equation with periodic boundary conditions across the channel. This nonlinear initial-boundary-value problem is investigated analytically and numerically. When surface-tension effects are negligible, the nonlinear response reaches a steady state and exhibits jump phenomena. On the other hand, in the high-surface-tension regime, no steady state is obtained. These results are discussed in connection with similar forced wave phenomena studied previously in a deepwater channel and related laboratory experiments. 相似文献
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Journal of Nonlinear Science - Consideration herein is a rotation-Camassa–Holm-type equation, which can be derived as an asymptotic model for the propagation of long-crested shallow-water... 相似文献
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A general method of solution of the hyperbolic partial differential equation governing the scattering of inertial waves in a rotating fluid is presented for the case of cylindrical scatterers with smooth convex cross-sections. The specific case of a parabolic cylinder is discussed in some detail. 相似文献
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Nonlinear Waves of Vorticity 总被引:1,自引:0,他引:1
This is a review of solutions of the vorticity equation for two-dimensional flow of an inviscid incompressible fluid that represent nonlinear waves. Geophysical applications are emphasized. Some of the solutions are valid in the beta-plane of Rossby. Some are related to weakly nonlinear perturbations of basic parallel flows and axisymmetric flows, to initial-value problems of hydrodynamic instability and to variational principles of minimal enstrophy or maximal entropy. Some have been found by exploiting well-known ideas of the theory of solitons. In addition to listing known solutions and presenting a synthesis of their relationship to other fluid dynamic results, we report a few new ideas and new solutions for strongly nonlinear waves. 相似文献
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The scattering of plane inertial waves by both a flat strip and a circular cylinder whose generators are perpendicular to the rotation vector is examined. The properties of the reflected and diffracted fields, viz. spatial decay, propagation, structure, etc....are contrasted with those of the classical scattering fields in the limit where the wave length is small compared to the size of the scatterer. 相似文献
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An analytical and numerical study is made of the propagation of waves whose wavenumbers are close to conditions for direct resonance. These waves emerge from the linear initial value problem as the dominant far field signal. The nonlinear evolution characteristics are investigated. It is found that weakly nonlinear waves at direct resonance may rapidly amplify and tend to become fully nonlinear in a finite time. 相似文献