A graphical representation of hyperelliptic KdV solutions

The periodic and quasi-periodic solutions of the integrable system have been studied for four decades based on the Riemann theta functions. However, there is a fundamental difficulty in representing the solutions graphically because the Riemann theta function requires several transcendental parameters. This paper presents a novel method for the graphical representation of such solutions from the algebraic treatment of the periodic and quasi-periodic solutions of the Baker-Weierstrass hyperelliptic $\mathrm{\wp }$ functions. We demonstrate the graphical representation of the hyperelliptic $\mathrm{\wp }$ functions of genus two.