Papers/Preprints
- Dynamics of KdV solitons in the presence of a slowly varying potential, preprint
pdf.
- (with
Galina Perelman
and
Maciej Zworski,
and an appendix by
Bernd Sturmfels)
Effective dynamics of double solitons for perturbed mKdV, preprint.
pdf.
The numerical illustrations
of the results and MATLAB codes can be found
here.
- (with
Rodrigo
Platte and
Svetlana Roudenko)
Blow-up criteria for the 3d cubic nonlinear Schroedinger equation
,
preprint.
pdf
- (with
Svetlana Roudenko)
Divergence of infinite-variance nonradial solutions to the 3d NLS
equation ,
to appear in Commun. Partial Differential Equations.
pdf
- (with
I. Bejenaru,
S. Herr, and
D. Tataru)
On the 2d Zakharov system with L^2 Schroedinger data,
Nonlinearity 22 (2009) pp. 1063--1089.
pdf
- (with Maciej Zworski)
Breathing patterns in nonlinear relaxation, Nonlinearity 22 (2009) pp. 1259--1301.
pdf
- (with Maciej Zworski)
Geometric structure of NLS evolution, unpublished.
pdf
- (with Nikos Tzirakis)
Asymptotically linear solutions in H^1 of the 2-d defocusing
nonlinear Schroedinger and Hartree equations, to appear in Journal of Hyperbolic Differential Equations.
pdf
- (with Kiril Datchev)
Fast soliton scattering by attractive delta impurities,
Commun. Partial Differential Equations 34 (2009) pp. 1074--1113
pdf
- (with
Thomas
Duyckaerts and Svetlana
Roudenko) Scattering for the non-radial 3d cubic nonlinear
Schroedinger equation,
Math. Res. Lett. 15 (2008) pp. 1233--1250.
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. 435--467.
pdf.
We have an unpublished erratum that
corrects an improper use of the Strichartz estimates in S 2.
- (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,
Trans. Amer. Math. Soc. 360 (2008), pp. 4619-4638.
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.
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