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SUMMARY:Construction of infinite-bump solutions for non-linear-Schrödinge
 r-like equations - Prof. Robert Magnus (Reykjavik/DPMMS)
DTSTART:20121022T140000Z
DTEND:20121022T150000Z
UID:TALK40673@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:In 1986 Floer and Weinstein gave a rigorous proof that a solut
 ion of the stationary\, one-dimensional\, cubic\, non-linear Schrödinger 
 equation\,\n\n_−ε^2^  u′′ + V(x)u − u^3^  = 0\,    −∞ < x < 
 ∞_\n\nexists that concentrates at a non-degenerate critical point of _V_
  as _ε → 0_. This means that the solution differs substantially from _0
 _ only in a small neighbourhood of the critical point. Y-G. Oh then constr
 ucted solutions that concentrate simultaneously at a finite set of non-deg
 enerate critical points\, the so-called multibump solutions. This work led
  to much interest in the concentration properties of solutions of this\, a
 nd more general equations\, in *R* ^n^ and with more general non-lineariti
 es. These have the form\n\n_−ε^2^ ∆u + F (V (x)\, u) = 0\,  x ∈ *R*
  ^n^_.\n\nIn this talk I shall discuss the construction of solutions that 
 concentrate simultaneously at an infinite set. I shall try to explain the 
 key ideas\, derived from PDE theory and functional analysis\, used in the 
 proofs.
LOCATION:CMS\, MR11
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