In this proceedings article we present a result on the 1-D cubic nonlinear Schrödinger equation with a sum of Dirac masses as initial data. We shall give a sketch of the proof. By using this result we show how to construct the evolution in time of a polygonal line through the binormal flow. This equation is a geometric flow for curves in and it is used as a model for the evolution of a vortex filament in fluid mechanics. These results were obtained in collaboration with Luis Vega in [4].
@article{SLSEDP_2017-2018____A3_0, author = {Valeria Banica}, title = {1-D cubic {NLS} with several {Dirac} masses as initial data and consequences}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:3}, pages = {1--9}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2017-2018}, doi = {10.5802/slsedp.118}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.118/} }
TY - JOUR AU - Valeria Banica TI - 1-D cubic NLS with several Dirac masses as initial data and consequences JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:3 PY - 2017-2018 SP - 1 EP - 9 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.118/ DO - 10.5802/slsedp.118 LA - en ID - SLSEDP_2017-2018____A3_0 ER -
%0 Journal Article %A Valeria Banica %T 1-D cubic NLS with several Dirac masses as initial data and consequences %J Séminaire Laurent Schwartz — EDP et applications %Z talk:3 %D 2017-2018 %P 1-9 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.118/ %R 10.5802/slsedp.118 %G en %F SLSEDP_2017-2018____A3_0
Valeria Banica. 1-D cubic NLS with several Dirac masses as initial data and consequences. Séminaire Laurent Schwartz — EDP et applications (2017-2018), Talk no. 3, 9 p. doi : 10.5802/slsedp.118. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.118/
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