Geodesic
Finite-gap solutions of~Abelian Toda chain of~genus~4 and 5 in~elliptic functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 1, pp. 11-21

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A reduction theorem is formulated and proved. Smooth real solutions of the abelian Toda lattice of the genus 4 and 5 are obtained in terms of the elliptic functions. In terms of the $g$-dimensional theta-functions the solutions of the genus $2g$ and $2g+1$ are constructed for the discrete Peierls–Fröhlich model in the absence of intramolecular deformation. 
@article{TMF_1989_78_1_a1,
     author = {A. O. Smirnov},
     title = {Finite-gap solutions {of~Abelian} {Toda} chain of~genus~4 and 5 in~elliptic functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {11--21},
     publisher = {mathdoc},
     volume = {78},
     number = {1},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_78_1_a1/}
}
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A. O. Smirnov. Finite-gap solutions of~Abelian Toda chain of~genus~4 and 5 in~elliptic functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 1, pp. 11-21. http://geodesic.mathdoc.fr/item/TMF_1989_78_1_a1/