Spectral theory of two-dimensional periodic operators and its applications

CONTENTS Introduction Chapter I. The spectral theory of the non-stationary Schrodinger operator § 1. The perturbation theory for formal Bloch solutions § 2. The structure of the Riemann surface of Bloch functions § 3. The approximation theorem § 4. The spectral theory of finite-gap non-stationary Schrodinger operators § 5. The completeness theorem for products of Bloch functions Chapter II. The periodic problem for equations of Kadomtsev-Petviashvili type § 1. Necessary information on finite-gap solutions § 2. The perturbation theory for finite-gap solutions of the Kadomtsev-Petviashvili –2 equation § 3. Whitham equations for space two-dimensional "integrable systems" § 4. The construction of exact solutions of Whitham equations § 5. The quasi-classical limit of two-dimensional integrable equations. The Khokhlov-Zabolotskaya equationChapter III. The spectral theory of the two-dimensional periodic Schrodinger operator for one energy level § 1. The perturbation theory for formal Bloch solutions § 2. The structure of complex "Fermi-curves" § 3. The spectral theory of "finite-gap operators with respect to the level E0" and two-dimensional periodic Schrodinger operators References

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