This summer school focuses on the stability of nonlinear waves in evolution equations. These special solutions arise in many applied problems where they model, for instance, water waves, nerve impulses in axons, or pulses in optical fibers. Understanding the dynamic stability of these waves is therefore a fundamental question in both theory and applications.
The program of the summer school begins with a short recap on the stability theory for fixed points in ordinary differential equations, providing the foundation for extending these ideas to nonlinear PDEs. The course then develops two complementary approaches: a Duhamel-based framework for dissipative PDEs, and a variational framework tailored to Hamiltonian systems. Both nonlinear stability approaches rely heavily on the spectral analysis of differential operators, for which the school will provide the necessary tools and techniques.