Applied partial differential equations and dynamical systems are my field of research. I am mostly interested in the analysis of existence, stability and interaction of localized structures such as fronts, pulses or wave packets. A recurring theme are reduction procedures inspired by invariant manifold and bifurcation theory such as center manifold reduction or the derivation of modulation equations. I have most experience with nonlinear wave equations from nonlinear optics and photonics, but also worked on reaction-diffusion systems and lattice equations. More recently, I developed interest in inverse spectral problems.
"Inverse spectral theory for uniformly open gaps in a weighted Sturm-Liouville problem"
M. Chirilus-Bruckner, C.E. Wayne. J. Math. Anal. Appl. 427 (2), p. 1168-1189 (2015)
"Butterfly catastrophe for fronts in a three-component reaction-diffusion system"
M. Chirilus-Bruckner, A. Doelman, P. van Heijster, J. Rademacher. J. Nonlinear Sci. 25 (1), p. 87-129 (2015)
"NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms"
M. Chirilus-Bruckner, W.-P. Düll, G. Schneider. Math. Nachr.288, (2-3), p. 158–166 (2015)
"sine-Gordon Equation:From Discrete to Continuum"
M. Chirilus-Bruckner, C. Chong, J. Cuevas, P.G. Kevrekidis. The sine-Gordon Model and its Applications. Nonlinear Systems and Complexity, 10 , p. 31-57 (2014)
"Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation"
M. Chirilus-Bruckner, W.-P. Düll, G. Schneider. J. Math. Anal. Appl. 414 (1), p. 166-175 (2014)
"Detection of standing pulses in periodic media by pulse interaction"
M. Chirilus-Bruckner, G. Schneider. J. Diff. Eq. 253 (7) p. 2161-2190 (2012)
"Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations"
M. Chirilus-Bruckner, Ch. Chong, O. Prill, G. Schneider. Disc. Cont. Dyn. Sys. 5 (5) p. 879-901 (2012)
- "Breather solutions in periodic media"
C. Blank, M. Chirilus-Bruckner, V. Lescarret and G. Schneider. Comm. Math. Phys. 302 (3) p. 815-841 (2011)
- "Standing generalized modulating pulse solutions for a nonlinear wave equation in periodic media"
V. Lescarret, C. Blank, M. Chirilus-Bruckner, Ch. Chong and G. Schneider. Nonlinearity 22 (8) p. 1869-1898 (2009)
- "Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves"
M. Chirilus-Bruckner, Ch. Chong, G. Schneider, H. Uecker. J. Math. Anal. Appl. 347 (1) p. 304-314 (2008)
- "A remark about the justification of the nonlinear Schrödinger equation in quadratic spatially periodic media"
C. Blank, M. Chirilus-Bruckner, Ch. Chong, V. Lescarret, G. Schneider and H. Uecker. ZAMP 59 (3) p. 554-557 (2008)
- "On the interaction of NLS-described modulating pulses with different carrier waves"
M. Chirilus-Bruckner, G. Schneider and H. Uecker. Math. Meth. Appl. Sci. 30 (15) p. 1965-1978 (2007)
"Interaction of oscillatory packets of water waves"
M. Chirilus-Bruckner, G. Schneider Dynamical Systems, Differential Equations and Appl., AIMS Proceedings (2015)
Nonlinear Waves (national MasterMath course) (Leiden University, 2017)
Analyse 4 (complexe functietheorie) (Leiden University, 2017)
Analyse 3 voor Natuurkunde/Sterrenkunde (Leiden University, 2016)
Analyse 4 (complexe functietheorie) (Leiden University, 2016)
Analyse 3 voor Natuurkunde/Sterrenkunde (Leiden University, 2015)
Mathematics Basic (Leiden University College, 2015)
MATH 2065 Introduction to Partial Differential Equations (Sydney University, 2014)
MATH 3078/3978 Partial Differential Equations and Waves (normal/advanced) (Sydney University, 2014)
MATH 1906 Mathematics (Special Studies Program) A (Sydney University, 2014)
MATH 2065 Introduction to Partial Differential Equations (Sydney University, 2013)
MA 242 Linear Algebra (Boston University, 2013)
APMA 0330 Methods of Applied Mathematics (Brown University, 2011)
Past Seminar Organization
- since November 2014
Assistant Professor at the Mathematical Institute, Leiden University, Leiden, The Netherlands
- July 2013 - October 2014
Lecturer at the School of Mathematics and Statistics, University of Sydney, Sydney, Australia
- January-June 2013
Lecturer at the Department of Mathematics and Statistics, Boston University, Boston, USA
Postdoc at the Department of Mathematics and Statistics, Boston University, Boston, and the Division of Applied Mathematics, Brown University, Providence, USA
Postdoc at the Centrum Wiskunde en Informatica, Amsterdam, the Netherlands
Doctoral Studies at the Fakultät für Mathematik, Universität Karlsruhe, Karlsruhe, Germany