The exact solution to the one-dimensional Poisson-Boltzmann equation with asymmetric boundary conditions

摘要

The exact solution to the one-dimensional Poisson-Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically, thus a numerical scheme has been applied.