Contact:

• Email: dohnal at kit dot edu

• Phone: +49-721-608 47670
• Fax: +49-721-608 46039
• Building/Floor/Room: Engesserstr. 6 / 2 / 211

Mailing Address:

Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung
Karlsruhe Institute of Technology
Engesserstr. 6
76128 Karlsruhe, Germany

Curriculum vitae: pdf file

Current / Recent Research Projects:

• moving breathers in a semilinear wave equation on a spatially periodic structure

• gap soliton asymptotics in Maxwell's equations for finite contrast photonic crystals
• existence of surface gap solitons at the interface of two periodic structures in the NLS
• linear stability of gap solitons via the numerical Evans function method
• conservative and stable discretizations of 1st order coupled mode equations

Research interests:

• nonlinear dispersive wave equations

• solitary waves in photonic band gap structures
• localized waves at surfaces
• modeling of nanotechnological processes, e.g. guiding, stopping, storing light
• asymptotic analysis of nonlinear waves
• Evans function for studying stability of solitary waves
• numerical computations of solitary waves via iterative methods
• perfectly matched layers in wave simulations

Collaborators:

• Alejandro Aceves

• Elisabeth Blank
• Yeo-Jin Chung
• Willy Doerfler
• Thomas Hagstrom
• Avner Peleg
• Dmitry Pelinovsky
• Michael Plum
• Wolfgang Reichel
• Guido Schneider
• Hannes Uecker

Publications:

Journal articles:

1. T. Dohnal and D. Pelinovsky, ``Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential,'' submitted to Phys. Rev. E, 2011. (arXiv:1110.3780)

2. T. Dohnal, M. Plum and W. Reichel, ``Surface gap soliton ground states for the nonlinear Schrödinger equation,'' Comm. Math. Phys. 308, 511-542 (2011). (arXiv:1011.2886)
3. E. Blank and T. Dohnal, "Families of Surface Gap Solitons and their Stability via the Numerical Evans Function Method," SIAM J. Appl. Dyn. Syst. 10, 667-706 (2011). (arXiv:0910.4858)
4. T. Dohnal and H. Uecker, ``Erratum to ``Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential'' by T. Dohnal and H. Uecker [Physica D 238 (2009), 860-879],'' Physica D 240, 357-362 (2011).
5. T. Dohnal, M. Plum and W. Reichel, ``Localized Modes of the Linear Periodic Schrödinger Operator with a Nonlocal Perturbation,'' SIAM J. Math. Anal. 41, 1967-1993 (2009). (arXiv:0811.4514)
6. T. Dohnal, ``Perfectly Matched Layers for Coupled Nonlinear Schrödinger Equations with Mixed Derivatives,'' J. Comput. Phys. 228, 8752–8765 (2009). (arXiv:0905.2321)
7. A. Peleg, Y. Chung, T. Dohnal, and Q. M. Nguyen, ``Diverging probability density functions for flat-top solitary waves,'' Phys. Rev. E 80:026602 (2009). (arXiv:0906.3001)
8. T. Dohnal and H. Uecker, ``Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential,'' Physica D 238, 860-879 (2009). (arXiv:0810.4499) Note: The arXiv version is a largely revised and corrected one.
9. T. Dohnal, D. Pelinovsky and G. Schneider, ``Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential,'' J. Nonlin. Sci. 19, 95-131 (2009). (arXiv:0707.3731)
10. T. Dohnal and D. Pelinovsky, ``Surface Gap Solitons at a Nonlinearity Interface," SIAM J. Appl. Dyn. Syst. 7, 249-264 (2008). (arXiv:0704.1742)
11. T. Dohnal and T. Hagstrom, ``Perfectly matched layers in photonics computations: 1D and 2D Nonlinear Coupled Mode Equations," J. Comput. Phys. 223, 690-710 (2007).
12. A.B. Aceves and T. Dohnal, ``Finite dimensional model for defect-trapped light in planar periodic nonlinear stuctures," Opt. Lett. 31, 3013-3015 (2006).
13. A. Peleg, T. Dohnal and Y. Chung, ``Effects of dissipative disorder on front formation in pattern forming systems,'' Phys. Rev. E 72:027203 (2005).
14. T. Dohnal and A.B. Aceves, ``Optical soliton bullets in (2+1)D nonlinear Bragg resonant periodic geometries,'' J. Yang, editor, Nonlinear Wave Phenomena in Periodic Photonic Structures, Studies in Applied Math. 115:209-232 (2005).

Conference proceedings:

1. A.B. Aceves and T. Dohnal, ``Stopping and bending light in 2D photonic structures,'' Proceedings of OSA topical meeting on Nonlinear Guided Waves and their Applications, Toronto, March 2004.

2. A.B. Aceves and T. Dohnal, ``Stopping and bending light in 2D photonic structures,'' in `` Nonlinear Waves: Classical and Quantum Effects,'' p. 293 - 302, F. Kh. Abdullaev and V.V. Konotop (eds.), Kluwer, 2004.

Dissertation:  T. Dohnal, Optical bullets in (2+1)D photonic structures and their interaction with localized defects, PhD dissertation, Univ. of New Mexico, 2005.

• avi movies accompanying the dissertation - interactions of 2D gap solitons with localized defects

Current and recent teaching:

• winter 2011/12: Introduction to the Numerics of PDEs

• winter 2010/11: Functional Analysis; Programming in Mathematics
• summer 2009: Applied Mathematics Seminar
• summer 2008:   Mathem. Modeling in Natural Sciences and Engineerinng (seminar)
• winter 2007/08: Mathem. Topics in Photonic Crystals
• summer 2007:    Inverse problems
• winter 2006/07:  Seminar: Theory and Numerics of Solitary Waves
• summer 2006:   Numerical mathematics II
• winter 2005/06:  Seminar on Geometric Numerical Integration

Short (professional) history:

• Jun. 2009 - now: postdoc at the Research Training Group -Analysis, Simulation and Design of Nanotechnological Processes, Karlsruhe Institute of Technology, Germany

• Oct. 2010 - Mar. 2011: visiting professor (Professurvertretung) - Department of Mathematics, University of Stuttgart, Germany

• Oct. 2007 -Jun. 2009: Humboldt Research Fellowship at the Institute for Applied and Numerical Mathematics and at the Research Training Group -Analysis, Simulation and Design of Nanotechnological Processes, University of Karlsruhe, Germany; host: Prof. Willy Doerfler

• Sep. 2005 - Oct. 2007: postdoc at the Seminar for Applied Mathematics ,  ETH  Zurich
                                   group of  Prof. Ralf Hiptmair

• 2001 - 2005 : PhD studies at the Department of Mathematics and Statistics,  University of New Mexico, USA 
     student of  Prof. Alejandro Aceves.
    dissertation: Optical bullets in (2+1)D photonic structures and their interaction with localized defects

ICIAM 07 Minisymposia: 
Strongly Nonlinear Phenomena in Optics, BECs, Hydrodynamics and Biology

My past institutions / sponsors:

Topical Links:

http://people.deas.harvard.edu/~jones/solitons/solitons.html

http://www.ma.hw.ac.uk/solitons/   -  so called "soliton homepage"

Alexander von Humboldt Foundation, Germany

Seminar for Applied Mathematics, ETH Zurich, Switzerland

Department of Mathematics and Statistics, University of New Mexico, USA

Los Alamos National Laboratory (Group T7), Los Alamos, New Mexico, USA

The Technical University in Liberec, Czech Republic

Nonprofessional history:

I am married and have two sons. I come from Jablonec nad Nisou, a town in the north of The Czech Republic. I was, however, born in Prostejovicky,  a tiny beautiful village in Moravia - the eastern part of the country. The village with about 280  people is close to a town called Prostejov .