Skip to Main Content

Applied Math Seminar: The NLS with Combined Nonlinearities by FIU Graduate Student Alex David Rodriguez

This is a past event.

Friday, February 25, 2022 at 4:00pm to 5:00pm

Virtual Event

Please join us remotely for a seminar by FIU graduate student Alex David Rodriquez.

Rodriguez considers the one-dimensional nonlinear Schrödinger equation iut + uxx + N (u) = 0, x, t ∈ R, with the nonlinearity term that is expressed as a sum of powers, possibly infinite: N (u) = Xcn|u| αn u, αn > 0. The combined nonlinearities appear in various physical applications such as chemical super fluidity, or the description of elementary particles such as bosons and defectons, or other subatomic structures, and in approximations of anisotropic media. We first investigate the local well-posedness of this equation for any positive powers of α in a certain weighted class of initial data, subset of H1 (R). Then, using the pseudoconformal transformation, we extend the local result to the global well-posedness. Furthermore, we investigate the asymptotic behavior of global solutions, those that have initial data with a quadratic phase e ib|x| 2 with sufficiently large positive b, in particular, we prove scattering of these solutions in H1 (R). One of the advantages of considering an infinite sum in the nonlinear term is the investigation of an exponential nonlinearity e α|u|u and its well-posedness in that case, the first such result. To conclude, we show numerical simulations in the focusing case for various cases of combined nonlinearities, including the exponential one, and investigate a threshold behavior for the global versus finite time existing solutions, which extends our theoretical results. This talk is based on the joint work with Gia Azcotia, Oscar Riano, Svetlana Roudenko and Hannah Wubben, which was initiated during the Research Experiences for Undergraduates program “AMRPU @ FIU” in Summer 2021.

Hosted by Hakima Bessiah.

Dial-In Information

Join Zoom Meeting

Meeting ID: 930 5388 4755
Passcode: AAM2022

Event Type

Academics, Lectures & conferences


Students, Faculty & Staff



Department of Mathematics and Statistics
Add to Calendar
Google Calendar iCal Outlook

Recent Activity

Statement of Free Expression

FIU endorses the Florida Board of Governors' Statement of Free Expression to support and encourage full and open discourse and the robust exchange of ideas and perspectives on our campuses. In addition to supporting this legal right, we view this as an integral part of our ability to deliver a high-quality academic experience for our students, engage in meaningful and productive research, and provide valuable public service. This includes fostering civil and open dialogue in support of critical thinking in and out of the classroom, including events hosted by the university.