Research

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 worked on various equation types ranging from nonlinear wave equations and reaction-diffusion systems to lattice equations and PDEs on graphs. What I find most intriguing is the impact of spatially varying coefficients on dynamics and, in this context, I have also developed interest in inverse spectral problems.

Publications

"The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation"

O. Jaibi, M. Chirilus-Bruckner, A. Doelman, E. Meron. 

Physica D 412 132637 (2020)

"Pulse solutions for an extended Klausmeier model with spatially varying coefficients"

R. Bastiaansen, M. Chirilus-Bruckner, A. Doelman. 

SIAM J. Appl. Dyn. Syst., 19(1):1–57 (2020)

 

"Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system"

M. Chirilus-Bruckner, P. van Heijster, J.D.M. Rademacher, H. Ikeda. 

J. Nonlinear Science 29 (6), p.2911-2953 (2019)

"Diffusive stability for periodic metric graphs"

M. Chirilus-Bruckner, D. Maier, G. Schneider. 

Math. Nach. 1–14 (2018)

 

"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.D.M. 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)

Proceedings

"Interaction of oscillatory packets of water waves" 

M. Chirilus-Bruckner, G. Schneider

Dynamical Systems, Differential Equations and Appl., AIMS Proceedings (2015)