Applied Math Seminar
The Applied Math Seminar hosts a wide range of talks in fields such as applied analysis, mathematical biology, fluid dynamics and electromagnetics, numerical computation, etc.
The seminar usually meets at 2:30pm on Fridays in room 1302 of Warren Weaver Hall.
Please email oneil@cims.nyu.edu with suggestions for speakers. If you would like to be added to the mailing list, please send an email to cimsams+subscribe@nyu.edu from the address at which you wish to receive announcements.
Seminar Organizer(s): Mike O'Neil
Upcoming Events

Friday, October 25, 20242:30PM, Warren Weaver Hall 1302
TBD
Gadi Fibich, Tel Aviv University 
Friday, November 8, 20242:30PM, Warren Weaver Hall 1302
On Novel Solitary Patterns in a Class of KleinGordon Equations
Philip Rosenau, TelAviv UniversitySynopsis:
We study the emergence, stability and evolution of solitons and compactons in a class of KleinGordon equations
\(u_{tt}  u_{xx} + u = u^{1+n}  \kappa_{1+2n} u^{1+2n}, \quad n= 1, 2, \ldots\)
endowed with trivial and nontrivial stable equilibria, and demonstrate that similarly to the classical \(\kappa_{1+2n} = 0\) cases, solitons are linearly unstable, but their instability weakens as \(\kappa_{1+2n}\) increases, and vanishes at a critical \(\kappa_{1+2n}^{crit} = (1+n)/(2+n)^2\), where solitons disappear and kinks form.
As the growing amplitude of the unstable soliton approaches the nontrivial equilibrium, it morphs into ”meson”, a robust box shaped sharp pulse with a flattop plateau which expands at a sonic speed. In the \(\kappa_{1+2n}^{crit}\) vicinity, where the instability is suppressed, and the internal modes hardly change, solitons persist for a very long time and rather than turn into meson, convert to breather.
Linear damping tempers the conversion and slows it. When \(1/2 < n < 0\), compactons emerge and being unstable morph either to meson or to breather.
Joint work with Slava Krylov.

Friday, December 6, 20242:30PM, Warren Weaver Hall 1302
TBA
Jennifer Crodelle, Middlebury College