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两个非线性方程的准确解 总被引:3,自引:0,他引:3
借助于计算机代数系统Mathematica利用直接代数方法获得了两个有数学物理意义的非线性耗散-色散方程的准确解,这种方法也适用于高维非线性方程。 相似文献
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Rajneesh Kumar Geeta Partap 《应用数学和力学(英文版)》2007,28(3):369-383
The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement. 相似文献
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本文采用一维流体模型导出了慢波介质自由电子激光器的线性色散方程,建立了电子和波相互作用的同向回旋同步机理和反向回旋同步机理. 相似文献
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非均匀平板波导的色散方程 总被引:6,自引:6,他引:0
利用转移矩阵理论分析了任意折射率分布平板波导的传输特性,导出了非均匀平板波导的近似解析色散方程,并指出了WKB近似的局限性,数值比较的结果表明,文中所得公式的精确度优于传统的WKB方法和其它近似方法。 相似文献
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Asymptotic large- and short-time behavior of solutions of the linear dispersion equation μt = Uxxx in IR× IR+, and its (2k+l)th-order extensions are studied. Such a refined scattering is based on a "Hermitian" spectral theory for a pair {B,B*} of non self-adjoint rescaled operators 相似文献