Two-gap elliptic solutions to integrable nonlinear equations

A. O. Smirnov

Matematičeskie zametki, Tome 58 (1995) no. 1, pp. 86-97.

Résumé

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.

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