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SUMMARY:On the inverse scattering method for integrable PDEs on graphs - V
 incent Caudrelier (City University London)
DTSTART:20160303T150000Z
DTEND:20160303T160000Z
UID:TALK62380@talks.cam.ac.uk
CONTACT:11300
DESCRIPTION:The inverse scattering method (ISM) is one of the major breakt
 hroughs in Mathematical Physics and Applied Mathematics. It provides a non
 linearization of the Fourier transform to solve certain (integrable) nonli
 near PDEs. But it also triggered entire new fields of research via its ext
 ension and consequences in areas areas other than analysis: geometry (clas
 sical r-matrix method\, Poisson-Lie groups) and algebra (quantum Yang-Baxt
 er equation\, quantum groups\, Lie bialgebras). The physical motivation of
  describing boundary conditions within ISM has led to\, and keeps triggeri
 ng\, its own share of discoveries in all these areas. To date\, in analysi
 s\, the most complete theory for dealing efficiently with boundary conditi
 ons in integrable PDEs is provided by the unified method of Fokas. I will 
 explain how the question of even more realistic situations where defects m
 ight be present as well naturally leads to consider PDEs on graphs. I will
  show how to use elements of Fokas method to solve in principle initial-bo
 undary value problems for PDEs on a star-graph. This is the first step of 
 a general program towards a theory of integrable PDEs on graphs. All along
 \, I will use the (cubic) nonlinear Schrödinger equation to illustrate th
 e ideas.
LOCATION:MR 14\, CMS
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