Martina Chirilus-Bruckner
P.O. Box 9512
2300 RA Leiden, THE NETHERLANDS
email: m.chirilus-bruckner -at- math.leidenuniv.nl
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 media on dynamics and, in this context, I have also developed interest in inverse spectral problems. The applications that have inspired my work in the past include optics/photonics and pattern formation in ecology. My most recent work concerns the emergence and control of chaotic dynamics in systems of reaction-diffusion equations.
Publications
"Chaotic fronts in a generalised Allen-Cahn-type model through a Shil'nikov bifurcation"
M. Chirilus-Bruckner, J.D.M. Rademacher, P. van Heijster
Preprint (2023)
"Breathers everwhere"
M. Chirilus-Bruckner.
Preprint (2023)
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)
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)
M. Chirilus-Bruckner, Ch. Chong, G. Schneider, H. Uecker.
J. Math. Anal. Appl. 347 (1) p. 304-314 (2008)
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)