Research Papers and Preprints
 (with Xuwen Chen) Well/illposedness bifurcation for the Boltzmann equation with constant collision kernel, preprint, arXiv:2206.11931.
 (with Zhiyuan Zhang) BenjaminOno soliton dynamics in a slowly varying potential revisited, SIAM J. Math. Anal. 54 (2022), no. 2, 2634–2690., arXiv:2106.02971.
 (with Xuwen Chen) Quantitative derivation and scattering of the 3D cubic NLS in the energy space, Ann. PDE 8 (2022), no. 2, Paper No. 11, 39 pp., arXiv:2104.06086.
 (with Xuwen Chen) The unconditional uniqueness for the energycritical nonlinear Schroedinger equation on T^4, Forum Math. Pi 10 (2022), Paper No. e3, 49 pp. arXiv:2006.05915.
 (with Luiz Gustavo Farah, Svetlana Roudenko, and Kai Yang) Asymptotic stability of solitary waves of the 3D quadratic ZakharovKuznetsov equation, to appear in American J of Math, arXiv:2006.00193.
 (with Riccardo Adami and Reika Fukuizumi) Scattering for the L2 supercritical point NLS, Trans. Amer. Math. Soc. 374 (2021), no. 1, 35–60. arXiv:1904.09066.
 (with Luiz Gustavo Farah, Svetlana Roudenko, and Kai Yang) Blowup in finite or infinite time of the 2D cubic ZakharovKuznetsov equation, preprint arXiv:1810.05121.
 (with Xuwen Chen) The derivation of the energycritical NLS from quantum manybody dynamics, Inventiones Mathematicae 217 (2019), no. 2, 433547. arXiv:1803.08082.
 (with Luiz Gustavo Farah and Svetlana Roudenko) Instability of solitons in the 2d cubic ZakharovKuznetsov equation, chapter in Fields Institute Communications 83 (Nonlinear Dispersive Partial Differential Equations and Inverse Scattering, editors: Miller, P.D., Perry, P., Saut, J.C., Sulem, C., ISBN13: 9781493998050). arXiv:1711.05907.
 (with Luiz Gustavo Farah and Svetlana Roudenko) Instability of solitons – revisited, II: The supercritical ZakharovKuznetsov equation, Nonlinear Dispersive Waves and Fluids, pp. 89–109, Contemp. Math., 725, Amer. Math. Soc., Providence, RI, 2019. arXiv:1711.03207.
 (with Luiz Gustavo Farah and Svetlana Roudenko) Instability of solitons – revisited, I: The critical generalized KdV equation. Nonlinear Dispersive Waves and Fluids, pp. 65–88, Contemp. Math., 725, Amer. Math. Soc., Providence, RI, 2019. arXiv:1711.03187.
 (with Chang Liu) Blowup for the 1D nonlinear Schroedinger equation with point nonlinearity II: Supercritical blowup profiles. Commun. Pure Appl. Anal. 20 (2021), no. 1, pp. 215242. arXiv:1708.03375.
 (with Chang Liu) Blowup for the 1D nonlinear Schroedinger
equation with point nonlinearity I: Basic theory, Journal of
Mathematical Analysis and Applications, Volume 483, Issue 1, 1 March 2020,
123522 pdf.
 (with Xuwen
Chen) The rigorous derivation of the 2D cubic focusing NLS
from quantum manybody evolution, Int Math Res Notices, first
published online June 30, 2016, doi:10.1093/imrn/rnw113, pdf.
 (with Xuwen
Chen) Correlation structures, manybody scattering processes and the derivation of the GrossPitaevskii hierarchy, Int Math Res Notices (2016) Vol. 2016, pp. 30513110, pdf.
 (with Xuwen
Chen)
Focusing quantum manybody dynamics II: the rigorous derivation of the 1D focusing cubic nonlinear Schroedinger equation from 3D,
Analysis & PDE 103 (2017), pp. 589633.
pdf.
 (with Xuwen
Chen)
Focusing quantum manybody dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schroedinger equation, Arch. Ration. Mech. Anal. 221 (2016), no. 2, pp. 631676, pdf.
 (with Xuwen
Chen)
On the KlainermanMachedon conjecture for quantum BBGKY hierarchy with
selfinteraction, J. Eur. Math. Soc. (JEMS) 18 (2016), no. 6, pp. 11611200, pdf.
 (with
Galina Perelman and
Svetlana Roudenko)
A solution to the focusing 3d NLS that blows up on a contracting
sphere, Trans. Amer. Math. Soc. 367 (2015), no. 6, pp. 38473872.
pdf.
 (with Xuwen
Chen)
On the rigorous derivation of the 2D cubic nonlinear Schroedinger equation from 3D quantum manybody dynamics, Archive for Rational Mechanics & Analysis 210 (2013) pp. 909954, pdf.
 (with
M. Christ
and
D. Tataru)
Low regularity a priori bounds for the modified Kortewegde Vries equation, Libertas Mathematica 32 (2012), pp. 5175, pdf.
 (with Quanhui Lin)
Phasedriven interaction of widely separated nonlinear Schroedinger
solitons, Journal of Hyperbolic Differential Equations 9 (2012) no. 03, pp. 511543, 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, IMRN International Math. Res. Notices (2011) vol. 2011, no. 23, pp. 53675397,
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.
