The method of Poincaré normal forms in problems of integrability of equations of evolution type

CONTENTS Introduction § 1. Changes of variables for evolution equations § 2. Analytic operators § 3. Existence of solutions § 4. Evolution equations in spaces with a basis § 5. Ancillary lemmas § 6. Poincare normalizing transformations § 7. Proof of Theorem 4.1 § 8. Non-linear heat and Schrodinger equations § 9. Generalizations of Theorem 4.1. Diffusion equation § 10. The Hopf-Cole substitution and the Miura transformation § 11. Concluding remarks References