Geodesic
Two-gap elliptic solutions to integrable nonlinear equations
Matematičeskie zametki, Tome 58 (1995) no. 1, pp. 86-97

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We study spectral surfaces associated with elliptic two-gap solutions to the nonlinear Schrödinger equation (NLS), the Korteweg-de Vries equation (KdV), and the sine-Gordon equation (SG). It is shown that elliptic solutions to the NLS and SG equations, as well as solutions to the KdV equation elliptic with respect to $t$, can be assigned to any hyperelliptic surface of genus 2 that forms a covering over an elliptic surface. 
@article{MZM_1995_58_1_a6,
     author = {A. O. Smirnov},
     title = {Two-gap elliptic solutions to integrable nonlinear equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {86--97},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_1_a6/}
}
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A. O. Smirnov. Two-gap elliptic solutions to integrable nonlinear equations. Matematičeskie zametki, Tome 58 (1995) no. 1, pp. 86-97. http://geodesic.mathdoc.fr/item/MZM_1995_58_1_a6/