Contact:
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Email: dohnal at kit dot edu
- Phone: +49-721-608 7670
- Fax: +49-721-608 6039
- Building/Floor/Room: Engesserstr. 6 / 2 / 211
Mailing Address:
Institut für Wissenschaftliches
Rechnen und Mathematische Modellbildung
Karlsruhe Institute of Technology
Kaiserstr. 12
76128 Karlsruhe, Germany
Curriculum vitae: pdf file
Current / Recent Research Projects:
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gap solitons in finite contrast non-separable periodic structures
- surface waves at a nonlinearity interface in 2D
- breathers in the 1D Coupled Mode Equations
- conservative and stable discretizations of 1st order coupled mode eqs
- linear stability of surface gap solitons via the Evans function method
Research interests:
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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
- coupled mode equations for waves in nonlinear periodic media
- nonlinear dispersive wave equations
- numerical computations of solitary waves via iterative methods
- numerical methods for nonlinear Hamiltonian PDE problems
- perfectly matched layers in wave simulations
Collaborators:
Publications:
Journal articles:
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E. Blank and T. Dohnal, "Continuation and Stability of Families of Surface Gap Solitons at a Nonlinearity Interface," submitted to SIAM J. Appl. Dyn. Syst., 2009. (arXiv:0910.4858)
- 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)
- T. Dohnal, ``Perfectly Matched Layers for Coupled Nonlinear Schrödinger Equations with Mixed Derivatives,'' J. Comput. Phys. 228, 8752–8765 (2009). (arXiv:0905.2321)
- 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)
- 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)
- 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)
- T. Dohnal and D. Pelinovsky, ``Surface Gap Solitons at a Nonlinearity Interface," SIAM J. Appl. Dyn. Syst. 7, 249-264 (2008). (arXiv:0704.1742)
- 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).
- A.B. Aceves and T. Dohnal, ``Finite dimensional model for defect-trapped light in planar periodic nonlinear stuctures," Opt. Lett. 31, 3013-3015 (2006).
- A. Peleg, T. Dohnal and Y. Chung, ``Effects of dissipative disorder on front formation in pattern forming systems,'' Phys. Rev. E 72:027203 (2005).
- 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:
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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.
- 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.
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avi movies accompanying the dissertation - interactions of 2D gap solitons with localized defects
