Tomas Dohnal
Tomáš Dohnal
Angewandte Analysis
Institut für Mathematik

### Contact:

Sprechstunde: Dienstags 11:00-12:00 und nach Vereinbarung

Tomáš Dohnal
Institut für Mathematik
Martin-Luther-Universität Halle-Wittenberg
06099 Halle (Saale), Germany

Current and recent teaching:

Halle:

• summer 2018: Measure Theory, Dispersive PDEs

Dortmund:

• waves, dispersive PDEs
• rigorous asymptotics of wavepackets in nonlinear problems
• solitary waves in periodic structures and at surfaces
• Evans function for studying stability of solitary waves
• PDE bifurcation problems
• bifurcation of nonlinear solutions from spectrum
• bifurcation in PT-symmetric (non-selfadjoint) problems
• numerics
• simulation of nonlinear waves
• bifurcation package PDE2PATH for elliptic PDEs
• perfectly matched layers for wave simulations

Collaborators:

PhD Students:

"WAS IST ...?" - talks for a broad math-audience

Publications:

Preprints:

1. T. Dohnal and D. Rudolf, NLS approximation for wavepackets in periodic cubically nonlinear wave problems in Rd,'' submitted, 2017. (
2. T. Dohnal and B. Schweizer, A Bloch wave numerical scheme for scattering problems in periodic wave-guides,'' submitted, 2017. (arXiv:1708.06427)
3. T. Dohnal and D. Pelinovsky, Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with PT-symmetry,'' accepted to Proc. R. Soc. Edinb. A, 2017. (arXiv:1702.0346)

Journal articles:

1. T. Dohnal and L. Helfmeier, Justification of the Coupled Mode Asymptotics for Localized Wavepackets in the Periodic Nonlinear Schrödinger Equation,'' J. Math. Anal. Appl. 450, 691-726 (2017). (arxiv:1602.04121)
2. T. Dohnal and P. Siegl, Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry,''  J. Math. Phys 57, 093502 (2016). (arXiv:1504.00054)
3. T. Bartsch, T. Dohnal, M. Plum and W. Reichel, Ground States of a Nonlinear Curl-Curl Problem in Cylindrically Symmetric Media,'' Nonlinear Differ. Equ. Appl. (2016) 23: 52. (arXiv:1411.7153)
4. T. Dohnal and H. Uecker, Bifurcation of Nonlinear Bloch Waves from the Spectrum in the Gross-Pitaevskii Equation,''  J. Nonlin. Sci. 26(3):581-618 (2016). (arXiv: 1409.4199)
5. T. Dohnal, A. Lamacz, and B. Schweizer, Dispersive homogenized models and coefficient formulas for waves in general periodic media,'' Asymptotic Analysis 93, 21-49 (2015). (arXiv:1401.7839)
6. T. Dohnal, A. Lamacz, and B. Schweizer, Bloch-wave homogenization on large time scales and dispersive effective wave equations,'' Multiscale Model. Simul. 12, 488-513 (2014). (arXiv:1302.4865)
7. T. Dohnal, Traveling Solitary Waves in the Periodic Nonlinear Schrödinger Equation with Finite Band Potentials,'' SIAM Appl. Math. 74, 306-321 (2014). (arXiv:1305.3504)
8. T. Dohnal, K. Nagatou, M. Plum and W. Reichel, Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schrödinger Equation,'' J. Math. Anal. Appl. 407 , 425-435 (2013). (arXiv:1202.3588)
9. T. Dohnal and W. Dörfler, Coupled Mode Equation Modeling for Out-of-Plane Gap Solitons in 2D Photonic Crystals,'' Multiscale Model. Simul. 11, 162-191 (2013). (arXiv:1202.3583)
10. T. Dohnal and D. Pelinovsky, Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential,'' Phys. Rev. E 85:026605 (2012). (arXiv:1110.3780)
11. 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)
12. 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)
13. 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).
14. 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)
15. T. Dohnal, Perfectly Matched Layers for Coupled Nonlinear Schrödinger Equations with Mixed Derivatives,'' J. Comput. Phys. 228, 87528765 (2009). (arXiv:0905.2321)
16. 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)
17. 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.
18. 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)
19. T. Dohnal and D. Pelinovsky, Surface Gap Solitons at a Nonlinearity Interface," SIAM J. Appl. Dyn. Syst. 7, 249-264 (2008). (arXiv:0704.1742)
20. 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).
21. A.B. Aceves and T. Dohnal, Finite dimensional model for defect-trapped light in planar periodic nonlinear stuctures," Opt. Lett. 31, 3013-3015 (2006).
22. A. Peleg, T. Dohnal and Y. Chung, Effects of dissipative disorder on front formation in pattern forming systems,'' Phys. Rev. E 72:027203 (2005).
23. 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. T. Dohnal, J. Rademacher, H. Uecker, D. Wetzel, pde2path 2.0: multi-parameter continuation and periodic domains, in H. Ecker, A. Steindl, S. Jakubek, eds, ENOC 2014 - Proceedings of 8th European Nonlinear Dynamics Conference, ISBN: 978-3-200-03433-4.
2. 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.
3. 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:  Optical bullets in (2+1)D photonic structures and their interaction with localized defects, PhD dissertation, Univ. of New Mexico, 2005.

Habilitation:   Localized Waves in Periodic Structures, Karslruhe Institute of Technology, May 2012.

Software Package:

• PDE2PATH, a Matlab package for continuation and bifurcation in 2D elliptic systems, with J. Rademacher, H. Uecker, and D. Wetzel. (manual also on arXiv)

### Short (professional) history:

Curriculum vitae: pdf file

 Past affiliations: Department of Mathematics, Technical University in Dortmund, Germany Department of Mathematics, Karlsruhe Institute of Technology, Germany 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 three kids. I come from Jablonec nad Nisou, a town in the north of the Czech Republic. I was, however, born in Prostejovicky,  a  beautiful village in Moravia - the eastern part of the country. The tiny village with about 280  people is close to a town called Prostejov .