Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems

CONTENTS Introduction § 1. Hyperbolic problems without dispersion. Asymptotic decomposition of a small amplitude solution into simple waves § 2. The method of averaging in hyperbolic problems without dispersion § 3. The method of matching in hyperbolic problems without dispersion § 4. Long waves in problems with weak dissipation § 5. Long waves in problems with small dispersion § 6. Small amplitude solutions in problems with strong dispersion § 7. Continuum limits of discrete equations on small amplitude solutions § 8. Asymptotic passages in non-one-dimensional waves § 9. Comments, problems References