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Abstract
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state solitary wave, and then the construction of new examples of non trivial multiple bubbles dynamics. Time permitting, I will extend the discussion to energy critical and super critical settingsI will review in this 3 hours class some results concerning the qualitative description of the flow for classical nonlinear dispersive PDE’s like the semilinear Schrodinger equation. I will start with recalling the basic structure and the notion of critical space. Soliton solutions will arise as fundamental nonlinear bubbles of energy and a special examples of compact solutions. Another example will be given by minimal blow up solutions which existence will be discussed. I will then review recent results concerning first the dynamical classification of the flow near the ground.
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