In the present paper we consider the nonlinear interaction of high frequency intense electromagnetic (EM) beam with degenerate electron plasmas. In a slowly varying envelop approximation the beam dynamics is described by the couple of nonlinear equations for the vector and scalar potentials. Numerical simulations demonstrate that for an arbitrary level of degeneracy the plasma supports existence of axially symmetric 2D solitons which are stable against small perturbations. The solitons exist if the power trapped in the structures, being the growing function of soliton amplitude, is above a certain critical value but below the value determining by electron cavitation. The robustness of obtained soliton solutions was verified by simulating the dynamics of initial Gaussian beams with parameters close to the solitonic ones. After few diffraction lengths the beam attains the profile close to the profile of the ground state soliton and propagates for a long distance without detectable distortion. The simulations have been performed for the input Gaussian beams with parameters far from ground state solutions. It is shown that the beam parameters are oscillating near the parameters of the ground soliton solution and thus the formation of oscillating waveguide structures takes place.
Multidimensional ion-acoustic solitary waves and shocks in quantum plasmas
研究了耗散量子等离子体中二维离子声孤立波和激波的非线性理论。色散的影响，所造成的电子和离子的电荷分离和量子力与Bohm势的简并电子，以及由于离子运动粘度的耗散被认为是。利用约化微扰技术，导出了量子等离子体中小振幅慢波系统演化的Kadomtsev-Petviashvili Burgers（KPB）型方程，得到了该方程的不同解，并进行了分析.结果表明，当粒子数密度满足$n_0\gtrless 1.3\times10^{31}$ cm $^{-3}$，其中$H$为电子等离子体激元能量与费米能量密度之比时，KPB方程可以允许压缩或稀疏的慢波.此外，数值研究了当电荷分离引起的波频散可以忽略时，大振幅定常激波的性质。它还表明，从单调振荡冲击的量子参数$H$的影响发生的过渡。
