Integrability and dynamics of the Poisson-Boltzmann equation in simple geometries
Integrability and dynamics of the Poisson-Boltzmann equation in simple geometries
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DOI：
10.1016/j.cnsns.2023.107668
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发表时间：
2023-11
期刊：
影响因子：
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通讯作者：
Kaiyin Huang;Shaoyun Shi;Shuangling Yang
中科院分区：
文献类型：
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作者：
Kaiyin Huang;Shaoyun Shi;Shuangling Yang
本文系统地研究了PB方程在平面、柱面和球面几何中的可积性和动力学性质。具体而言，PB方程与单物种和零永久电荷，明确的解决方案是在平面和圆柱几何，而非可积性的球几何证明了微分伽罗瓦方法。此外，我们建立了一个稳定的流形上的PB方程的非紧的直线解，提供了一个统一的动力系统的角度来看问题的单电荷膜。值得注意的是，在平面几何形状的情况下，我们的研究结果表明，凹向上的微分电容曲线的轮廓产生的阴离子和阳离子之间的相互作用存在于电解质中，而不是PB方程的鞍形结构。
In this article, we conduct a systematic study of the integrability and dynamics of the PB equation in plane, cylinder and sphere geometries. Specifically, for the PB equation with single species and zero permanent charges, explicit solutions are available in the plane and cylinder geometries, while non-integrability in the sphere geometry is demonstrated by the differential Galoisian approach. Furthermore, we establish a stable manifold result on a noncompact straight-line solution of the PB equation, providing a unified dynamical system perspective on the problem of single charged membrane. Notably, in the case of plane geometry, our results reveal that the concave-upward profile of the differential capacitance curve arises from the interplay between anions and cations present in the electrolyte, as opposed to the saddle structure of the PB equation.