Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Communications in Nonlinear Science and Numerical Simulation
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.