Existence of chaos 
            in perturbed cubic nonlinear Schroedinger equation

                                   by

                             Yanguang (Charles) Li
                  Princeton Institute for Advanced Studies


               INSCC 110, 3:30pm  Monday, February 8, 1999


                               Abstract


              First I will present machineries from isospectral 
              which enable to establish Melnikov analysis for the
              perturbed soliton equation. Then I will present 
              machineries from infinte dimensional dynamical 
              systems -- Fenichel fibers for the perturbed 
              soliton equation. Next I will present a measurement
              inside a slow manifold, which together with the 
              Melnikov measurement to estblish the existence of 
              homoclinic orbits. For the second part, I will 
              construct Smale horseshoes in the neighborhood 
              of the homoclinic orbits. First I will present 
              smooth linearization tools. Then I will present 
              a fixed point theorem. Finally I will construct 
              Smale horseshoes through Conley-Moser criteria
              --- deterministic chaos.
                                

Request for preprints and reprints to Yanguang (Charles) Li <cli@IAS.EDU>

This information can be found at http://www.math.utah.edu/research/