The Kirchhoff elastic rod, the nonlinear Schrödinger equation, and DNA supercoiling

Abstract

We have derived a time-independent, one-dimensional nonlinear Schrödinger equation for the stationary state configurations of supercoiled DNA. The effect of DNA self-contact has been included analytically. For the cases of non-self-contact and periodic boundary conditions, closed-form solutions have been obtained which describe the stationary state configurations of supercoiled DNA.