Publications and Preprints

For the interested student/researcher: The most updated pdf files can be located on the web-pages of the particular journals that my papers have appeared.

• (with E. Compaan) Uniqueness theory for initial-boundary value problems for KdV type equations and systems of equations, in preparation.
  

• (with B. Erdogan, and T. B. Gurel ) The Fifth Order KP--II Equation on the Upper Half--plane, submitted, pdf file.
  

• (with E. Compaan), Sharp well--posedness for the generalized KdV of order three on the half line, submitted to Physica D, pdf file.
  

• (with E. Compaan) ,  Low regularity global well-posedness for the Klein-Gordon-Schrodinger system on the half line, Discrete Contin. Dyn. Syst. 39 (2019), no. 7, 3867--3895, pdf file.

• (with B. Erdogan, and T. B. Gurel) The derivative nonlinear Schrodinger equation on the half line, Ann. Inst. H. Poincare Anal. Non Lineaire 35 (2018), no. 7, 1947-1973 pdf file.
  

• (with B. Erdogan, and T. B. Gurel) Smoothing for the fractional Schrodinger equation on the torus and the real line, Indiana Univ. Math. J. 68 (2019), no. 2, 369-392 pdf file.
  

• (with B. Erdogan) Well-posedness theory for the Zakharov system on the half-line, Commun. Partial Differential Equations 42 (2017) no. 7, 1121-1149, pdf file.

• (with E. Compaan) Well-posedness and nonlinear smoothing for the "good" Boussinesq equation on the half-line, J. Differential Equations 262, (2017), 5824--5859, pdf file.
  

• (with B. Erdogan) Dispersive Partial Differential Equations: Wellposedness Theory and Applications, Book, Cambridge Student Texts, Cambridge University Press.

• (with B. Erdogan) Regularity Properties of the cubic nonlinear Schrodinger equation on the half line, J. Funct. Anal. 271 (2016), no. 9, 2539--2568,  pdf file.
  

• (with V. Chousionis and B. Erdogan) Fractal solutions of the vortex filament equation, Proc. Lond. Math. Soc (3) 110 (2015), no. 3. 543--564 , pdf file.

• (with B. Erdogan and J. Marzuola) The structure of global attractors for dissipative Zakharov systems with forcing on the torus, to appear in SIAM J. Appl. Dyn. Syst. 14 (2015), no. 4, 1978-1990, pdf file.

• (with B. Erdogan, and S. Demirbas) Existence and uniqueness theory for the fractional Schrodinger equation on the torus. Some topics in harmonic analysis and applications, 145–162, Adv. Lect. Math. (ALM), 34, Int. Press, Somerville, MA, 2016, pdf file.

• (with B. Erdogan and V. Zharnitsky) Near-linear dynamics for shallow water waves, pdf file.

• (with B. Erdogan) Talbot effect for the cubic nonlinear Schrodinger equation on the torus, Mathematical Research Letters 20 (2013) no. 6, 1081--1090, pdf file.

• Smoothing properties for dispersive partial differential equations and systems of equations, Report on Oberwolfach Workshop ID 1220, May 2012: Nonlinear Evolution equations.

• (with B. Erdogan) Smoothing and global attractors for the Zakharov system on the torus, Anal. PDE, 6 (2013), no. 3, 723--750, pdf file.

• (with B. Erdogan and V. Zharnitsky) High frequency perturbation of cnoidal waves in KdV, SIAM J. Math. Anal. 44 (2012), no. 6, 4147--4164, pdf file.

• (with B. Erdogan) Long time dynamics for the forced and weakly damped KdV equation on the torus, Commun. Pure Appl. Anal. 12 (2013), no. 6, 2669--2684,  pdf file.

• (with T. Chen and N. Pavlovic) Multilinaer Morawetz identities for the Gross-Pitaevskii hierarchy, Contemp. Math., 581, Amer. Math. Soc, (2012), 39--62, pdf file

• (with B. Erdogan) Global Smoothing for the Periodic KdV Evolution, Int. Math. Res. Not. IMRN 2013, no. 20, 4589--4614, pdf file.

• (with B. Erdogan and V. Zharnitsky) Nearly linear dynamics of nonlinear dispersive waves, Phys. D 240 (2011) no. 17, 1325--1333, pdf file.

• (with D. De Silva, N. Pavlovic and G.Staffilani), Correction to "Global well-posedness and polynomial bounds for the defocusing nonlinear Schrodinger equation in 1d, Comm. Partial Differential Equations 33 (2008), no. 7-9, 1395--1429", Comm Partial Differential Equations 36 (2011), no. 2, 293--303, pdf file.

• (with T. Chen and N. Pavlovic) Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies, Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010), no. 5, 1271--1290, pdf file.

• (with J. Colliander and M. Grillakis) Remarks on global a priori estimates for the nonlinear Schrodinger equation, Proc. Amer. Math. Soc. 138 (2010), no. 12, 4359--4371, pdf file.

• (with B. Erdogan and V. Zharnitsky) Near-linear dynamics in KdV with periodic boundary conditions, Nonlinearity 23 (2010), no. 7, 1675--1694, pdf file.

• (with Justin Holmer) Asymptotically linear solutions in $H^1$ of the 2-d defocusing nonlinear Schrodinger and Hartree equations, J. Hyperbolic Differ. Equ. 7 (2010), no. 1, 117--138, pdf file.

• (with J. Colliander and M. Grillakis) Tensor products and correlation estimates with applications to nonlinear Schrodinger equations, Comm. Pure Appl. Math. 62 (2009), no. 7, 920--968, pdf file.

• (with J. Colliander and M. Grillakis) Improved interaction Morawetz inequalities for the cubic nonlinear Schrodinger equation in 2d, Int. Math. Res. Not. IMRN 2007, no. 23, Art. ID rnm090, 30 pp., pdf file.

• (with D. De Silva, N. Pavlovic and G.Staffilani) Global well-posedness and polynomial bounds for the defocusing nonlinear Schrodinger equation in 1d, Comm. Partial Differential Equations 33 (2008), no. 7-9, 1395--1429., pdf file.

• (with J. Colliander and J. Holmer) Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrodinger systems, Trans. Amer. Math. Soc. 360 (2008), no. 9, 4619--4638., pdf file.

• (with D. De Silva, N. Pavlovic and G.Staffilani) Global Well-Posedness for the L^2-critical nonlinear Schrodinger equation in higher dimensions, Communications on Pure and Applied Analysis, 6 (2007), no. 4, 1023--1041, pdf file.

• (with D. De Silva, N. Pavlovic and G.Staffilani) Global well-posedness for a periodic nonlinear Schrodinger equation in 1d and 2d, Discrete and Continuous Dynamical Systems, Series A. 19 (2007), no. 1, 37--65, pdf file.

• Mass concentration phenomenon for the quintic nonlinear Schrodinger equation in one dimension. SIAM J. Math. Anal. 37 (2006), no. 6, 1923--1946, pdf file.

• (with P. G. Kevrekidis) On the collapse arresting effects of discreteness. Math. Comput. Simulation 69 (2005), no. 5-6, 553--566.

• The Cauchy problem for the Klein-Gordon-Schrodinger system in low dimensions below the energy space. Comm. Partial Differential Equations 30 (2005), no. 4-6, 605--641.
  

• (with Arpad Benyi) Multilinear almost diagonal estimates and applications. Studia Math. 164 (2004), no. 1, 75--89.