DG-MP-PDE Seminar: Ian Zwiers (UBC)

  • Date: 09/28/2010
Ian Zwiers (UBC)

University of British Columbia


Blowup of the cubic focusing nonlinear Schrodinger equation in dimension two with vortex soliton profile


Vortex solitons are standing wave solutions with complex phase that is an (integer) multiple of the angular polar coordinate. This multiple we call the 'spin', and indexes a family of solutions with increasing L2 norm. In the case of no spin, Merle and Raphael have shown that there exists a range of data that blowup with the Townes profile (the regular soliton) and whose H1 norm grows at a precise 'log-log' rate. We prove that in the case of spin 1, there is comparable data that blows up with the vortex profile and the log-log rate. The case of spin 2 and 3 will be discussed. This is joint work with Gideon Simpson (Toronto)


3:30pm - 4:30pm, WMAX 216