标题： 上混合波与尘埃离子磁声波在尘埃等离子体中的相互作用及稳定二维孤子的形成 显示英文标题

标题： Interaction of upper hybrid waves with dust-ion-magnetoacoustic waves and stable two-dimensional solitons in dusty plasmas

摘要： 我们得到了一个二维非线性方程组，用于描述沿外部磁场垂直传播的上混合波与磁化尘埃等离子体中的尘埃离子磁声（DIMA）波之间的相互作用，该方程组包括静电势包络和低频磁场扰动。这些方程包含标量和矢量非线性。推导出非线性色散关系，并获得了衰减和调制不稳定性阈值及增长率。数值估计表明，在实际尘埃等离子体中，不稳定性阈值很容易被超过。在静态（亚音速）近似下，通过广义Petviashvili松弛方法数值求解得到了二维（2D）孤立子解（基态）。孤立子中的磁场和等离子体密度扰动在空间上是非单调的，除了像井一样的扰动形式外，还有扰动凸起。这种特殊的径向孤立子轮廓与以前关于二维孤立子的结果有显著不同。关键点是由于Rao截止频率导致DIMA波色散中存在间隙，使得非线性具有非局部性。我们证明了由于非局部非线性，在固定能量下哈密顿量有下界，从而证明了基态的稳定性。 显示英文摘要

摘要： We obtain a two-dimensional nonlinear system of equations for the electrostatic potential envelope and the low-frequency magnetic field perturbation to describe the interaction of the upper hybrid wave propagating perpendicular to an external magnetic field with the dust-ion-magnetoacoustic (DIMA) wave in a magnetized dusty plasma. The equations contain both scalar and vector nonlinearities. A nonlinear dispersion relation is derived and the decay and modulation instability thresholds and growth rates are obtained. Numerical estimates show that instability thresholds can easily be exceeded in real dusty plasmas. In the static (subsonic) approximation, a two-dimensional (2D) soliton solution (ground state) is found numerically by the generalized Petviashvili relaxation method. The perturbations of the magnetic field and plasma density in the soliton are nonmonotonic in space and, along with the perturbation in the form of a well, there are also perturbation humps. Such peculiar radial soliton profiles differ significantly from previously known results on 2D solitons. The key point is that the presence of a gap in the DIMA wave dispersion due to the Rao cutoff frequency causes the nonlinearity to be nonlocal. We show that due to nonlocal nonlinearity the Hamiltonian is bounded below at fixed energy, proving the stability of the ground state.