Research Papers and Preprints
 (with Chang Liu) Blowup for the 1D nonlinear Schroedinger
equation with point nonlinearity I: Basic theory, preprint pdf.
 (with Xuwen
Chen) The rigorous derivation of the 2D cubic focusing NLS
from quantum manybody evolution, preprint, pdf.
 (with Xuwen
Chen) Correlation structures, manybody scattering processes and
the derivation of the GrossPitaevskii hierarchy, preprint, pdf.
 (with Xuwen
Chen)
Focusing quantum manybody dynamics II: the rigorous derivation of the
1D focusing cubic nonlinear Schroedinger equation from 3D,
preprint,
pdf.
 (with Xuwen
Chen)
Focusing quantum manybody dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schroedinger equation, preprint pdf.
 (with Xuwen
Chen)
On the KlainermanMachedon conjecture for quantum BBGKY hierarchy with
selfinteraction, to appear in J. Eur. Math. Soc. (JEMS) pdf.
 (with
Galina Perelman and
Svetlana Roudenko)
A solution to the focusing 3d NLS that blows up on a contracting
sphere, to appear in Transactions of the AMS, preprint pdf.
 (with Xuwen
Chen)
On the rigorous derivation of the 2D cubic nonlinear Schroedinger equation from 3D quantum manybody dynamics, to appear in Archive for Rational Mechanics and Analysis, preprint pdf.
 (with
M. Christ
and
D. Tataru)
Low regularity a priori bounds for the modified Kortewegde Vries equation,
to appear in Libertas Mathematica (new series),
preprint pdf.
 (with Quanhui Lin)
Phasedriven interaction of widely separated nonlinear Schroedinger
solitons, to appear in Journal of Hyperbolic Differential Equations,
pdf.
 (with Svetlana
Roudenko)
Blowup solutions on a sphere for the 3d quintic NLS in the energy
space, Analysis & PDE 53 (2012), pp. 475512,
pdf.
 (with Svetlana
Roudenko)
A class of solutions to the 3d cubic nonlinear Schroedinger
equation that blowup on a circle, AMRX Appl Math Res Express (2011)
2011 (1): 2394, doi: 10.1093/amrx/abq016,
pdf.
 Dynamics of KdV solitons in the presence of a slowly varying
potential, to appear in IMRN
Internat. Math. Res. Notices,
pdf.
 (with
Galina Perelman
and
Maciej Zworski,
and an appendix by
Bernd Sturmfels)
Effective dynamics of double solitons for perturbed mKdV,
Communications in Mathematical Physics 305 (2011) pp. 363425,
pdf.
The numerical illustrations of the results and MATLAB codes can be found
here.
 (with
Rodrigo Platte and
Svetlana Roudenko)
Blowup criteria for the 3d cubic nonlinear Schroedinger equation
,
Nonlinearity 23 (2010) pp. 9771030.
pdf
 (with
Svetlana Roudenko)
Divergence of infinitevariance nonradial solutions to the 3d NLS
equation ,
Commun. Partial Differential Equations 35 (2010) pp. 878905.
pdf
 (with
I.
Bejenaru,
S. Herr, and
D. Tataru)
On the 2d Zakharov system with L^2 Schroedinger data,
Nonlinearity 22 (2009) pp. 10631089.
pdf
 (with Maciej Zworski)
Breathing patterns in nonlinear relaxation, Nonlinearity 22 (2009) pp. 12591301.
pdf
 (with Maciej Zworski)
Geometric structure of NLS evolution, unpublished.
pdf
 (with Nikos Tzirakis)
Asymptotically linear solutions in H^1 of the 2d defocusing
nonlinear Schroedinger and Hartree equations, Journal
of Hyperbolic Differential Equations 7 (2010) pp. 117138.
pdf
 (with Kiril Datchev)
Fast soliton scattering by attractive delta impurities,
Commun. Partial Differential Equations 34 (2009) pp. 10741113
pdf
 (with
Thomas
Duyckaerts and Svetlana
Roudenko) Scattering for the nonradial 3d cubic nonlinear
Schroedinger equation,
Math. Res. Lett. 15 (2008) pp. 12331250.
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, Comm. Math. Phys. 282 (2008) pp. 435467.
pdf.
We have an unpublished erratum that
corrects an improper use of the Strichartz estimates in S 2.
 (with Svetlana Roudenko)
On blowup 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. 689718. 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. 467489.
pdf.
 (with Jeremy
Marzuola and Maciej
Zworski) Soliton splitting by external delta potentials,
J. Nonlinear Science 17 (2007), pp. 349367. 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 wellposedness for the Zakharov and
KleinGordonSchroedinger systems,
Trans. Amer. Math. Soc. 360 (2008), pp. 46194638.
pdf.
 Local illposedness of the 1d Zakharov system, Electron. J.
Differential Equations, Vol. 2007(2007), No. 24, pp. 122. pdf
 (with Jeremy
Marzuola and Maciej
Zworski) Fast soliton scattering by delta impurities,
Comm. Math. Phys. 274 (2007), pp. 187216. pdf
 The initialboundary value problem for the Kortewegde Vries
equation, Comm. Partial Differential Equations 31
(2006), pp. 11511190. pdf
 The initialboundary value problem for the 1d nonlinear
Schroedinger equation on the halfline, Differential Integral
Equations 18 (2005), pp. 647668. pdf
 Ph.D. Thesis, University of Chicago, 2004. Uniform estimates for
the Zakharov system and the initialboundary value problem for the
Kortewegde Vries and nonlinear Schroedinger equations. 210 pages.
pdf. Ph.D. Thesis summary. 10 pages. pdf.
