An algebro-geometric model for the shape of supercoiled DNA II

Following the previous paper (Matsutani and Previato, Physica D {\bf{430}} (2022) 133073), the hyperelliptic solutions of generalized elastica of genus three are investigated; its curvature obeys the modified (MKdV) KdV equation. This paper demonstrates a novel construction of the hyperelliptic solutions of the MKdV equation over $\mathbb{R}$ based on an amazing relation for the real solutions. We illustrated the hyperelliptic solutions of the generalized elastica numerically. The shapes reproduce a property of shapes, modulation of a repeat of figure eight and inverse of {\lq}S\rq, of supercoiled DNAs.