Nonlinear Waves Seminar - Pavel Lushnikov

Pavel Lushnikov, Department of Mathematics, University of New Mexico

Tail minimization principle in wave collapse

Wave collapse  occurs in numerous nonlinear physical systems resulting in catastrophic self-focusing of laser beams in optical media, collapse of Bose-Einstein condensate and white foam formation on the crests of oceanic waves.   Underlying equations for all these diverse effects are two-dimensional nonlinear Schrodinger equation (NLSE) and its nonlocal extension, Davey-Stewartson equation (DSE). We find that collapses in both NLSE and  DSE obey the tail minimization principle when physical systems dynamically choose  self-similar-type solutions which minimize the spatial tails of the collapsing solution on the border of the spatial collapsing region. Qualitatively similar minimization occurs in the collapse in  Keller-Segel equation of bacterial aggregation.  This minimization ensures that the singularity (collapse)  reaches in fastest possible time (propagation distance for optical applications) because the maximum optical power (in optical applications) or number of particles (in Bose-Einstein condensate) are captured in the collapsing region. A weak escape of particles (optical power) from that region is controlled by an analog of quantum tunneling resulting both for NLSE and DSE in square root time dependence of spatial scaling  with double logarithmic modification. We found that such scaling is asymptotically dominant only after the amplitude of collapsing solution reaches double-exponentially large amplitudes of the solution ~10^10^100, which is unrealistic to achieve in either physical experiments or numerical simulations. In contrast, we developed a detailed an asymptotic theory which is valid starting from quite moderate (about 3 fold) increase of the solution amplitude compared with the initial conditions.

Dial-In Information

Tuesday, January 25, 2022 at 4:00pm to 5:00pm

Virtual Event
Event Type

Colloquium/Seminar

Interests

Science & Technology, Research & Innovation

Audience

Students, Graduate Students

College, School & Unit

Engineering & Applied Science

Tags

nonlinear waves seminar

Group
Applied Mathematics
Add to Calendar
GoogleiCalOutlook

Recent Activity