Geodesic
Heat Equations and Families of Two-Dimensional Sigma Functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 5-32

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In the framework of S. P. Novikov's program for boosting the effectiveness of theta-function formulas of finite-gap integration theory, a system of differential equations for the parameters of the sigma function in genus 2 is constructed. A counterpart of this system in genus 1 is equivalent to the Chazy equation. On the basis of the obtained results, a two-dimensional analog of the Frobenius–Stickelberger connection is defined and calculated. 
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     author = {E. Yu. Bunkova and V. M. Buchstaber},
     title = {Heat {Equations} and {Families} of {Two-Dimensional} {Sigma} {Functions}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {5--32},
     publisher = {mathdoc},
     volume = {266},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_266_a0/}
}
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E. Yu. Bunkova; V. M. Buchstaber. Heat Equations and Families of Two-Dimensional Sigma Functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 5-32. http://geodesic.mathdoc.fr/item/TM_2009_266_a0/