This volume contains expanded versions of lecture notes of CIMPA's school held in Lanzhou in July 2004. These texts offer a detailed survey, including the most recent advances, of some topics in analysis of partial differential equations arising from physics, mechanics and geometry such as Korteweg-de Vries equation, harmonic maps, Birkhoff normal form and KAM theorem for infinite dimensional dynamical systems, vorticity of Euler equation, semi-classical analysis of Schrödinger and Dirac equations, and limiting situations of semilinear elliptic equations. They are mainly aimed at students and young researchers interested in these subjects.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in differential equations.

Table of Contents

• B. Grébert -- Birkhoff normal form and Hamiltonian PDEs
• F. Hélein -- Four lambda stories, an introduction to completely integrable systems
• D. Iftimie -- Large time behavior in perfect incompressible flows
• D. Robert -- Propagation of coherent states in quantum mechanics and applications
• W.-M. Wang -- Stability of quantum harmonic oscillator under time quasi-periodic perturbation
• X. P. Wang -- Microlocal estimates of the stationary Schrödinger equation in semi-classical limit
• D. Ye -- Some limiting situations for semilinear elliptic equations