Justin Holmer

Papers/Preprints

• (with Nikos Tzirakis) Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations, preprint. pdf
  
  
• (with Kiril Datchev) Fast soliton scattering by attractive delta impurities, preprint. pdf
  
  
• (with Thomas Duyckaerts and Svetlana Roudenko) Scattering for the non-radial 3d cubic nonlinear Schroedinger equation, to appear, Math. Res. Lett. pdf
  
  
• (with Maciej Zworski) Soliton interaction with slowly varying potentials, IMRN Internat. Math. Res. Notices 2008 (2008), Art. ID runn026, 36 pp. pdf
  
  
• (with Svetlana Roudenko) A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation, to appear, Comm. Math. Phys. pdf
  
  
• (with Svetlana Roudenko) On blow-up solutions to the 3d cubic nonlinear Schroedinger equation, AMRX Appl. Math. Res. Express 2007 (2007), Art. ID abm004, 29 pp. pdf
  
  
• (with Maciej Zworski) Slow soliton interaction with delta impurities, J. Modern Dynamics 1 (2007), pp. 689--718. pdf.
  
  
• (with J. Colliander, M. Visan, and X. Zhang) Global existence and scattering for rough solutions to generalized nonlinear Schroedinger equations on R, Commun. Pure Appl. Anal. 7 (2008), no. 3, pp. 467--489. pdf.
  
  
• (with Jeremy Marzuola and Maciej Zworski) Soliton splitting by external delta potentials, J. Nonlinear Science 17 (2007), pp. 349-367. pdf.
  This is a numerical companion to our paper, Fast soliton scattering by delta impurities, posted below.
  
  
• (with James Colliander and Nikolaos Tzirakis) Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schroedinger systems, to appear, Trans. Amer. Math. Soc. pdf.
  
  
• Local ill-posedness of the 1d Zakharov system, Electron. J. Differential Equations, Vol. 2007(2007), No. 24, pp. 1-22. pdf
  
  
• (with Jeremy Marzuola and Maciej Zworski) Fast soliton scattering by delta impurities, Comm. Math. Phys. 274 (2007), pp. 187-216. pdf
  
  
• The initial-boundary value problem for the Korteweg-de Vries equation, Comm. Partial Differential Equations 31 (2006), pp. 1151-1190. pdf
  
  
• The initial-boundary value problem for the 1d nonlinear Schroedinger equation on the half-line, Differential Integral Equations 18 (2005), pp. 647-668. pdf
  
  
• Ph.D. Thesis, University of Chicago, 2004. Uniform estimates for the Zakharov system and the initial-boundary value problem for the Korteweg-de Vries and nonlinear Schroedinger equations. 210 pages. pdf. Ph.D. Thesis summary. 10 pages. pdf.

Courses

• Fall 2007, Math 202A. Introduction to Topology and Analysis I.
• Spring 2008, Math 222B. Partial Differential Equations.

Other Materials

• Lecture notes for the Park City Math Institute graduate summer school course "The Cauchy problem for the Quasilinear Schrodinger equation," delivered by Carlos Kenig, July 13-18, 2003. These notes are authored by Carlos Kenig. Revised June 2005, 125 pages. pdf.