Publications of Christof Sparber

Paolo Antonelli, Remi Carles and Christof Sparber.  On nonlinear Schrödinger type equations with nonlinear damping.  Int. Math. Res. Not., 2015(3):740--762, 2015.
A. Figalli, C. Klein, P. Markowich and C. Sparber.  WKB analysis of Bohmian dynamics.  Comm. Pure Appl. Math., 67(4):581--620, 2014. MR3168122
J. L. Bona, G. Ponce, J.-C. Saut and C. Sparber.  Dispersive blow-up for nonlinear Schrödinger equations revisited.  J. Math. Pures Appl. (9), 102(4):782--811, 2014. MR3258130
Christian Klein, Christof Sparber and Peter Markowich.  Numerical study of fractional nonlinear Schrödinger equations.  Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 470(2172):20140364, 26, 2014. MR3269035
Paolo Antonelli, Jean-Claude Saut and Christof Sparber.  Well-posedness and averaging of NLS with time-periodic dispersion management.  Adv. Differential Equations, 18(1-2):49--68, 2013. MR3052710
Michael Hintermüller, Daniel Marahrens, Peter A. Markowich and Christof Sparber.  Optimal bilinear control of Gross-Pitaevskii equations.  SIAM J. Control Optim., 51(3):2509--2543, 2013. MR3069086
Paolo Antonelli, Daniel Marahrens and Christof Sparber.  On the Cauchy problem for nonlinear Schrödinger equations with rotation.  Discrete Contin. Dyn. Syst., 32(3):703--715, 2012. MR2851876
Rémi Carles and Christof Sparber.  Semiclassical wave packet dynamics in Schrödinger equations with periodic potentials.  Discrete Contin. Dyn. Syst. Ser. B, 17(3):759--774, 2012. MR2873114
Christian Hainzl, Mathieu Lewin and Christof Sparber.  Ground state properties of graphene in Hartree-Fock theory.  J. Math. Phys., 53(9):095220, 27, 2012. MR2905802
Rémi Carles and Christof Sparber.  Nonlinear dynamics of semiclassical coherent states in periodic potentials.  J. Phys. A, 45(24):244032, 14, 2012. MR2930527
Peter Markowich, Thierry Paul and Christof Sparber.  On the dynamics of Bohmian measures.  Arch. Ration. Mech. Anal., 205(3):1031--1054, 2012. MR2960039
Anton Arnold, Irene M. Gamba, Maria Pia Gualdani, Stéphane Mischler, Clement Mouhot and Christof Sparber.  The Wigner-Fokker-Planck equation: stationary states and large time behavior.  Math. Models Methods Appl. Sci., 22(11):1250034, 31, 2012. MR2974172
Rémi Carles, Eric Dumas and Christof Sparber.  Geometric optics and instability for NLS and Davey-Stewartson models.  J. Eur. Math. Soc. (JEMS), 14(6):1885--1921, 2012. MR2984591
Christian Klein and Christof Sparber.  Transverse stability of periodic traveling waves in Kadomtsev-Petviashvili equations: a numerical study.  In Recent advances in harmonic analysis and partial differential equations, pages 155--168.  Amer. Math. Soc., Providence, RI, 2012. MR3013057
Christof Sparber.  Semiclassical quantum dynamics and Bohmian trajectories.  Int. Math. Nachr., 219:1--11, 2012.
Paolo Antonelli and Christof Sparber.  Existence of solitary waves in dipolar quantum gases.  Phys. D, 240(4-5):426--431, 2011. MR2748730
Shi Jin, Peter Markowich and Christof Sparber.  Mathematical and computational methods for semiclassical Schrödinger equations.  Acta Numer., 20:121--209, 2011. MR2805153
Gonca L. Aki, Jean Dolbeault and Christof Sparber.  Thermal effects in gravitational Hartree systems.  Ann. Henri Poincaré, 12(6):1055--1079, 2011. MR2823208
Zhongyi Huang, Peter A. Markowich and Christof Sparber.  Numerical simulation of trapped dipolar quantum gases: collapse studies and vortex dynamics.  Kinet. Relat. Models, 3(1):181--194, 2010. MR2580959
Rémi Carles, Eric Dumas and Christof Sparber.  Multiphase weakly nonlinear geometric optics for Schrödinger equations.  SIAM J. Math. Anal., 42(1):489--518, 2010. MR2607351
Peter Markowich, Thierry Paul and Christof Sparber.  Bohmian measures and their classical limit.  J. Funct. Anal., 259(6):1542--1576, 2010. MR2659771
Johannes Giannoulis, Alexander Mielke and Christof Sparber.  High-frequency averaging in semi-classical Hartree-type equations.  Asymptot. Anal., 70(1-2):87--100, 2010. MR2731651
Paolo Antonelli and Christof Sparber.  Global well-posedness for cubic NLS with nonlinear damping.  Comm. Partial Differential Equations, 35(12):2310--2328, 2010. MR2763357
Zhongyi Huang, Shi Jin, Peter A. Markowich and Christof Sparber.  Bloch decomposition-based method for high frequency waves in periodic media.  In Some problems on nonlinear hyperbolic equations and applications, pages 161--188.  Higher Ed. Press, Beijing, 2010. MR2816450
Irene M. Gamba, Maria Pia Gualdani and Christof Sparber.  A note on the time decay of solutions for the linearized Wigner-Poisson system.  Kinet. Relat. Models, 2(1):181--189, 2009. MR2472154
Zhongyi Huang, Shi Jin, Peter A. Markowich and Christof Sparber.  On the Bloch decomposition based spectral method for wave propagation in periodic media.  Wave Motion, 46(1):15--28, 2009. MR2477041
Gianluca Panati, Christof Sparber and Stefan Teufel.  Geometric currents in piezoelectricity.  Arch. Ration. Mech. Anal., 191(3):387--422, 2009. MR2481065
Hailiang Liu and Christof Sparber.  Rigorous derivation of the hydrodynamical equations for rotating superfluids.  Math. Models Methods Appl. Sci., 18(5):689--706, 2008. MR2413034
Johannes Giannoulis, Alexander Mielke and Christof Sparber.  Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential.  J. Differential Equations, 245(4):939--963, 2008. MR2427402
Zhongyi Huang, Shi Jin, Peter A. Markowich and Christof Sparber.  Numerical simulation of the nonlinear Schrödinger equation with multidimensional periodic potentials.  Multiscale Model. Simul., 7(2):539--564, 2008. MR2443002
Rémi Carles, Peter A. Markowich and Christof Sparber.  On the Gross-Pitaevskii equation for trapped dipolar quantum gases.  Nonlinearity, 21(11):2569--2590, 2008. MR2448232
Gonca L. Aki, Peter A. Markowich and Christof Sparber.  Classical limit for semirelativistic Hartree systems.  J. Math. Phys., 49(10):102110, 10, 2008. MR2464606
Zhongyi Huang, Shi Jin, Peter A. Markowich and Christof Sparber.  A Bloch decomposition-based split-step pseudospectral method for quantum dynamics with periodic potentials.  SIAM J. Sci. Comput., 29(2):515--538 (electronic), 2007. MR2306256
Christian Klein, Christof Sparber and Peter Markowich.  Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation.  J. Nonlinear Sci., 17(5):429--470, 2007. MR2361416
Lukas Neumann and Christof Sparber.  Stability of steady states in kinetic Fokker-Planck equations for bosons and fermions.  Commun. Math. Sci., 5(4):765--777, 2007. MR2375045
Christof Sparber.  Effective mass theorems for nonlinear Schrödinger equations.  SIAM J. Appl. Math., 66(3):820--842 (electronic), 2006. MR2216722
Zhongyi Huang, Shi Jin, Peter Markowich, Christof Sparber and Chunxiong Zheng.  A time-splitting spectral scheme for the Maxwell-Dirac system.  J. Comput. Phys., 208(2):761--789, 2005.
Christian Hainzl, Mathieu Lewin and Christof Sparber.  Existence of global-in-time solutions to generalized Dirac-Fock type evolution equation.  Lett. Math. Phys., 72(2):99--113, 2005.
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