Title：Stability of periodic waves in integrable equations
Abstract：Many Hamiltonian PDEs are integrable with the inverse scattering transform method. In particular, they exhibit infinitely many conserved quantities, Backlund-Darboux transformations, solvability with the associated linear systems, and other properties. I will show how to use these properties in order to study the stability problems of periodic waves which cannot be solved in general nonintegrable Hamiltonian PDEs. The key examples include modulational stability of periodic waves in the defocusing NLS and the transverse stability of periodic waves in the KP-II equation.
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