Algebro-geometric solutions to the modified Sawada-Kotera hierarchy (Q2872477)

In this paper the modified Sawada-Kotera (SK) hierarchy associated with a \(3 \times 3\) matrix spectral problem is derived. The discussion relies on solving the Lenard recursion equation and the zero-curvature equation. Using the characteristic polynomial of the Lax matrix for the modified SK hierarchy, the authors introduce a trigonal curve \(K_{m-1}\) and they also give the corresponding Baker-Akhiezer function and a meromorphic function on it. With the help of the property of the Baker-Akhiezer function and the asymptotic expansions of the meromorphic function, their explicit Riemann theta function is derived. Algebro-geometric solutions of the entire modified Sawada-Kotera hierarchy are obtained using an asymptotic expansion of the meromorphic function and its Riemann theta function representation. As an application, some simple examples are given.