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The final-state problem for the cubic-quintic NLS with non-vanishing boundary conditions
PDE and Applied Math Seminar| Speaker: | Jason Murphy, UC Berkeley |
| Location: | 3106 MSB |
| Start time: | Thu, Nov 12 2015, 4:10PM |
In this talk, I will discuss recent joint work with R. Killip and M. Visan on the cubic-quintic nonlinear Schr\"odinger equation with non-vanishing boundary conditions in three space dimensions. In particular, we construct global solutions with prescribed scattering states. Our arguments build on work of Gustafson, Nakanishi, and Tsai on the related Gross--Pitaevskii equation. The presence of the energy-critical (quintic) nonlinearity and changes in the geometry of the energy functional add some new difficulties to the problem.