共查询到18条相似文献,搜索用时 93 毫秒
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本文基于Jacobi椭圆函数和Lamé方程,应用摄动法研究了非线性与立方非线性Schrodinger方程,获得了其新的多级包络周期解。这些解在极限条件下可以退化为各种形式的包络孤波解。 相似文献
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本文基于Jacobi椭圆函数和Lamé方程,应用摄动法研究了非线性与立方非线性Schrodinger方程,获得了其新的多级包络周期解。这些解在极限条件下可以退化为各种形式的包络孤波解。 相似文献
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本文给出了普遍的规一化束流包络函数方程,这种方程可以用来描述加速系统和传输系统中相对论束流及非相对论束流的包络和发射度形状的变化。文中阐述了在考虑加速过程和束流空间电荷效应的情况下,这些包络函数方程的近似求解方法,导出了近似解的表达式。 相似文献
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Nonlinear quantum theory of interaction of charged particles and monochromatic radiation in a medium
G. K. Avetisyan A. Kh. Bagdasaryan G. F. Mkrtchyan 《Journal of Experimental and Theoretical Physics》1998,86(1):24-31
We study the quantum theory of nonlinear interaction of charged particles and a given field of plane-transverse electromagnetic
radiation in a medium. Using the exact solution of the generalized Lamé equation, we find the nonlinear solution of the Mathieu
equation to which the relativistic quantum equation of particle motion in the field of a monochromatic wave in the medium
reduces if one ignores the spin-spin interaction (the Klein-Gordon equation).We study the stability of solutions of the generalized
Lamé equation and find a class of bounded solutions corresponding to the wave function of the particle. On the basis of this
solution we establish that the particle states in a stimulated Cherenkov process form bands. Depending on the wave intensity
and polarization, such a band structure describes both bound particle-wave states (capture) and states in the continuous spectrum.
It is obvious that in a plasma there can be no such bands, since bound states of a particle with a transverse wave whose phase
velocity v
ph is higher than c are impossible in this case. The method developed in the paper can be applied to a broad class of problems reducible to the
solution of the Mathieu equation.
Zh. éksp. Teor. Fiz. 113, 43–57 (January 1998) 相似文献
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By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schrfdinger type equations. It is shown that many exact periodic solutions of some nonlinear Schro^edinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions. 相似文献
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The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate tothe envelope shock wave solutions and/or the envelope solitary wave solutions. 相似文献
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By using the solutions of an auxiliary Lam\'e equation, a direct algebraic method is
proposed to construct the exact solutions of $N$-coupled nonlinear Schr\"{o}dinger
equations. The abundant higher-order exact periodic solutions of a family of
$N$-coupled nonlinear Schr\"{o}dinger equations are explicitly obtained with the aid
of symbolic computation and they include corresponding envelope solitary and shock
wave solutions. 相似文献