We have derived a generalized one-dimensional time-independent nonlinear Schrödinger equation for the stationary state configurations of supercoiled DNA, based on an elastic rod model which includes deformations of bending, twisting, shear, and extension. Closed-form solutions for the axis of DNA have been obtained in terms of elliptic functions and elliptic integrals. These solutions describe the stationary state configurations of supercoiled DNA.
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Shi et al. (1995) studied this question.
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