To provide an up-to-date intensive course on methods to establish stability of solitary waves for Schrodinger and wave type equations. The equations and models of this type have important applications in different fields: quantum mechanics, biology, medicine. The main goal of the school is to introduce Master Degree Students and PhD Students to the main math tools to study the asymptotic behavior (stability and instability) of the solitary and travelling wave and to have contact and to make mini projects in collaboration with established specialists in the field from Europe, USA and Japan.

· Target group:

the Course is oriented preferentially to students and PhD students in Mathematics and Physics.

Weak for possible preliminary work on arguments supposed to be known: 12-17 May 2014, arguments sopposed to be known:  Linear, nonlinear stability for ordinary differential equations and classical fields modeled with evolution partial differential equations, asymptotic stability and a priori estimates to establish asymptotic stability, spectral theory.

Intensive week: Daily intensive lecturing (6 hours / day from May 19th to May 23th, Monday to Friday), among lecturer: Israel Sigal, Andrew Comech

Workshop week: Daily intensive lecturing from May 26th to June 1th, Monday to Friday),

Week of individual work on suggesting and introducing to some concrete mini projects: individual work with tutors in the week 2-6 June.

The school will provide an overall number of 6 credits (after attendance of the overall Course and submission of a small project within December 31st, 2014. Partial attendance to the Course will give right to a number of credits proportionally reduced.