Date:	Wed, October 7, 2015
Time:	11:15
Place:	Research I Seminar Room

Abstract: This work is a contribution to the study of nonlinear Schrödinger equations (NLS). Such equations arise in many physical fields, including nonlinear optics and Bose-Einstein condensation. This work contains three connected themes. The first part constructs multi-soliton solutions of the Gross-Pitaevskii, as an approximate superposition of traveling waves (solitons). This result is obtained by exploiting the integrability of the the Gross-Pitaevskii equation. The second part clarifies the relations between the classical formulation and the so-called hydrodynamical formulation that only has a meaning when the solution does not vanish anywhere in the spatial domain. Generalizations for the multidimensional equation are established too. The last part of this work concerns existence and uniqueness results for a family of quasi-linear partial differential equations that generalize the equation of the binormal curvature flow for a curve in the three-dimensional space. The latter equation is in connection to the focussing cubic NLS by Hasimoto transformation.