双离子尘埃等离子体中的离子声孤子
Ion-Acoustic Solitons in Bi-Ion Dusty Plasma
摘要：
从理论上研究了含两种离子的尘埃等离子体中离子声孤子的传播。利用基于Korteveg-de-Vries方程的方法，证明了区分压缩孤子和稀疏孤子存在区域的负离子密度的临界值连续地依赖于尘埃密度。在小参数展开式的高阶形式下，导出了修正的临界密度Korteveg-de Vries方程。发现该方程的非线性系数对任意尘埃密度和正负离子质量都为正。对于负离子密度接近其临界值的情况下，孤立子的解决方案被发现，同时考虑到二次和三次非线性。用拟势方法研究了任意振幅孤立波的传播。结果表明，正负势孤立波同时存在的临界值附近的尘埃密度范围较宽。
英文摘要：
The propagation of ion-acoustic solitons in a warm dusty plasma containing two ion species is investigated theoretically. Using an approach based on the Korteveg-de-Vries equation, it is shown that the critical value of the negative ion density that separates the domains of existence of compressi- on and rarefaction solitons depends continuously on the dust density. A modified Korteveg-de Vries equation for the critical density is derived in the higher order of the expansion in the small parameter. It is found that the nonlinear coefficient of this equation is positive for any values of the dust density and the masses of positive and negative ions. For the case where the negative ion density is close to its critical value, a soliton solution is found that takes into account both the quadratic and cubic nonlinearities. The propagation of a solitary wave of arbitrary amplitude is investigated by the quasi-potential method. It is shown that the range of the dust densities around the critical value within which solitary waves with positive and negative potentials can exist simultaneously is relatively wide.
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