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Invariant measures and the soliton resolution conjecture

New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015

October 22, 2015 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Sourav Chatterjee (Stanford University)
Location: MSRI: Simons Auditorium
  • discrete NLS on a torus

  • ergodic components

  • soliton solutions

  • sub-critical mass

  • Birkhoff's ergodicity theorem

  • existence of global solutions

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



I will talk about the micro-canonical invariant measure for the discrete nonlinear Schrödinger equation on a torus in the mass-subcritical regime, and prove that a random function drawn from this measure is close to the ground state soliton with high probability. This proves that “almost all” ergodic components of this flow have the property of convergence to a soliton in the long run, which is a statistical variant of what is sometimes called the soliton resolution conjecture

24941?type=thumb Chatterjee_Notes 480 KB application/pdf Download
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