Methods of Algebraic Geometry in the Theory of Non-Linear Equations

CONTENTS Introduction § 1. The Akhiezer function and the Zakharov-Shabat equations § 2. Commutative rings of differential operators § 3. The two-dimensional Schrödinger operator and the algebras associated with it § 4. The problem of multi-dimensional -algebraic operators Appendix 1. The Hamiltonian formalism in equations of Lax and Novikov types Appendix 2. Elliptic and rational solutions of the K-dV equations and systems of many particles Concluding Remarks References