The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems

Abstract

CONTENTS Introduction Chapter I. Integrability conditions § 1. Formal symmetries and conservation laws § 2. The technique of formal series § 3. Canonical conservation laws and divergency conditions Chapter II. Evolution equations of the second order § 4. Invertible transformations § 5. The classification theorem Chapter III. Enlargement of the module of invertible substitutions § 6. Generalized contact transformations § 7. Partial differentiations and potentiations § 8. Transformations of symmetric systems Chapter IV. Integrable systems of Schrödinger type § 9. The list of integrable equations § 10. A description of symmetric systems. Tests for integrability § 11. A brief bibliographical comment References