Finite-Gap Integration of the Gerdjikov-Ivanov Equation: a Classical Method

Abstract

We present a classical algebro-geometric method to construct exact quasi-periodic solutions for the Gerdjikov-Ivanov (GI) equation. Using Baker-Akhiezer functions on hyperelliptic curves, explicit solutions are derived by Riemann theta functions through asymptotic and spectral analysis. Compatibility with the Lax pair ensures integrability, while spectral curve geometry and divisor theory extend finite-gap integration to higher-genus settings.

Keywords

Riemann surface / Baker-Akhiezer function / Algebro-geometric solution / 35C07

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Shanghai University