Homepage of Vivi Rottschäfer



Mathematisch Instituut
Universiteit Leiden
P.O. Box 9512
2300 RA Leiden

kamer 206
tel. 071-5277113





I am `universitair hoofd docent' (associate professor) in the research group Analysis and Dynamical Systems, financed by a VIDI-grant by the Dutch Science Organisation NWO.
My research interests are in dynamical systems and partial differential equations.

PhD students


In 2006, I was awarded a VIDI-grant by the Dutch Science Organisation NWO.
This grant is titled `Formation of singularities in natural systems' and started on 1 January 2007.
A summary and more information of the research can be found here.


Dynamical systems seminar 2015 Patterns and waves

Course 2015 Introduction to Perturbation Methods

Course 2014  Introduction to Dynamical Systems

Dynamical systems seminar 2014 Introduction to stochastic differential equations (with applications)

Course 2014  Bifurcations and Chaos

Course 2013 Introduction to Dynamical Systems

Dynamical Systems Seminar 2013 Maps

Course 2012 Introduction to Perturbation Methods

Seminarium 2012   Amplitude vergelijkingen

Course 2012 Bifurcations and Chaos

Seminarium 2011   Bifurcations with a slowly varying parameter

Course 2011 Introduction to Perturbation Methods

Course 2010 Introduction to Pattern Formation

Applied Analysis 2007

Dynamical Systems and Nonequilibrium Pattern Formation, spring 2003

Onderwijsweek `Stabiliteitsanalyse in PDV's' bij het Thomas Stieltjes Institute for Mathematics
gehouden van 3 - 7 maart 2003.



Journal articles

Q.-X.Liu, A. Doelman, V. Rottschäfer, M. de Jager, P. M. J. Herman, M. Rietkerk, J. van de Koppel (2013), Phase separation explains a new class of self-organized spatial patterns in ecological systems,
Proc. Natl. Acad. Sci. (PNAS), 110 (29), pp. 11905-11910.
Vivi Rottschäfer (2012) Asymptotic analysis of a new type of multi-bump, self-similar,
blowup solutions of the Ginzburg Landau equation, European Journal of Applied
matics, Vol. 24 Nr. 1, pp. 103 - 129.

Vivi Rottschäfer (2008) Multi-bump, self-similar, blowup solutions 
of the Ginzburg Landau equation, Physica D, Vol. 237, pp. 510 - 539.
Geertje Hek,  Vivi Rottschäfer (2007), Semiconductor laser with filtered optical feedback: from optical injection to conventional feedback, IMA J. of Applied Mathematics, Vol. 72, pp. 420 - 450.
Vivi Rottschäfer, Bernd Krauskopf (2007) The ECM-backbone of the Lang-Kobayashi equations: a geometric picture,  J. of Bifurcation and Chaos, Vol. 17 Nr. 5, pp. 1 - 14.
C.J. Budd, V. Rottschäfer, J.F. Williams (2005) Multi-bump, blow-up, self-similar solutions of the complex Ginzburg-Landau equation, SIAM J. on Applied Dynamical Systems,
4, Nr. 3, pp. 649 - 678

Lambertus A. Peletier, Vivi Rottschäfer (2004) Pattern selection of solutions of the Swift-Hohenberg equation, Physica D, Vol. 194, pp. 95 - 126.
Vivi Rottschäfer, Tasso Kaper (2003)  Geometric theory for multi-bump, self-similar, blowup solutions of the cubic nonlinear Schrödinger equation, Nonlinearity, Vol. 16, Nr. 3, pp. 929 - 961.
L. A. Peletier, Vivi Rottschäfer (2002) Large time behaviour of solutions of the Swift-Hohenberg equation, Comptes Rendu Mathematique, Vol. 336, Nr. 3, pp. 225 - 230.
Jeff Hasty, Milos Dolnik, Vivi  Rottschäfer, James J. Collins (2002) Synthetic gene network for entraining and amplifying cellular oscillations,  Physical Review Letters, 88, pp  148101. See also the Virtual Journal of Biological Physics Research.
Vivi Rottschäfer, Tasso Kaper (2002) Blowup in the nonlinear Schrödinger equation near critical dimension, JMAA, Vol. 268, Nr. 2, pp. 517 - 549.
V. Rottschäfer, C. E. Wayne (2001) Existence and stability of traveling fronts in the extended Fisher-Kolmogorov equation, Journal of Differential Equations, Vol. 176, Nr. 2, pp. 532 - 560.
V. Rottschäfer (2001) Multi-bump patterns by a normal form approach ,  Discrete and continuous dynamical systems Series B, Vol. 1, Nr. 3,  pp. 363 - 386.
V. Rottschäfer, A. Doelman (1998) On the transition of the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation, Physica D, Vol. 118, pp. 261 - 292.
A. Doelman, V. Rottschäfer (1997)  Singularly perturbed and non-local modulation equations for systems with interacting instability mechanisms, J. Nonl. Sc., Vol. 7, pp.  371 - 409.


V. Rottschäfer (1998) Co-dimension 2 phenomena in pattern formation, 
Ph. D. -thesis, University Utrecht.

D.R. Pik, V. Rottschäfer (eds.) (2004)  Proceedings of the fourty-fifth European Study Group with Industry, ISBN 90-9017846-5
Contributions to books and Conference proceedings

Neil Budko, Alessandro Corbetta, Bert van Duijn, Sander Hille, Oleh Krehel, Vivi Rottschäfer,
Linda Wiegman, Delyan Zhelyazov (2013) A Simple model for O2 transport and consumption
in germinating seeds, Proceedings of the ninetieth European Study Group with

Paulo J. De Andrade Serra, Tasnim Fatima, Andrea Fernandez, Tim Hulshof, Tagi Khaniyev,
Patrick J.P. van Meurs, JanJaap Oosterwijk, Stefanie Postma, Vivi Rottsch
äfer, Lotte Sewalt,
Frits Veerman (2012) Up and Beyond - Building a mountain in the Netherlands,
Proceedings of the eighty-fourth European Study Group with Industry, pp 104 -125.

Vivi Rottschäfer (2010) De uitdagende vraagstukken van bedrijven, Vakantiecursus 2010
Wiskunde: de uitdaging, CWI syllabus 60, pp. 55 - 64.

Simon van Mourik, Joris Bierkens, Hans Stigter, Martijn Dirkse, Karel Keesman, Vivi
Rottschäfer (2009) DHV water pumping optimization,

Proceedings of the sixty-seventh European Study Group with Industry
, 99 --116
Niels Besseling, Onno Bokhove, Alla Kolechkina, Jaap Molenaar, Ronald van Nooyen,
Vivi Rottschäfer, Alfred Stein, Anton Stoorvogel (2008) Math Fights Flooding,
 Proceedings of the sixty-third European Study Group with Industry,  47 -- 63.
Vincent Creigen,  Luca Ferracina,  Andriy Hlod,  Simon van Mourik, Krischan Sjauw,
Vivi Rottschäfer, Michel Vellekoop, Paul Zegeling (2007) Modeling a Heart Pump,
 Proceedings of the fifty-eighth European Study Group with Industry, 7 -- 25.
V. Rottschäfer  (2006) Patronen blijven fascineren, Over de grenzen van het weten,
jaarboek 2004, Vereniging van Akademie-onderzoekers,  93 -- 96.
 JF Williams, Geertje Hek, Alistair Vardy, Vivi Rottschäfer, Jan Bouwe van den Berg, Joost Hulshof (2005) Mathematical Techniques for Neuromuscular Analysis,  Proceedings of the fifty-second European Study Group with Industry, 109 -- 127.

Geertje Hek, Vivi Rottschäfer (2005) Semiconductor laser with filtered optical feedback: bridge between conventional feedback and optical injectionProceedings ENOC-2005, Eindhoven, Netherlands, 2015-2024.
Vivi Rottschäfer, Bernd Krauskopf (2005) A three-parameter study of external cavity modes in semiconductor lasers with optical feedback, Proceedings of the  Fifth IFAC Workshop on Time-Delay Systems, eds. W. Michiels, D. Roose, Elsevier, 239-244.
Chris Budd, Robbert Fokkink, Geertje Hek, Peter van der Kamp,  Derk Pik, Vivi Rottschäfer (2004) Hanging a carillon in a broek-system, Proceedings 45th Eur. Study Group Ind.
Vivi Rottschäfer (2003) Wiskunde voor de rozenkweker, Vakantiecursus 2003 Wiskunde in het dagelijks leven, CWI syllabus  52, 15-26.
O. Bokhove, J.L.A. Dubbeldam, P. Getto, B. van 't Hof , N.C. Ovenden, D.R. Pik, G. Prokert,  V. Rottschäfer, D. van der Sar (2002) Roses are unselfish: a greenhouse growth model to predict harvest ratesProceedings 42nd Eur. Study Group Ind.
(G.M. Hek ed.) CWI syllabus 51
V. Rottschäfer (2000) Co-dimension 2 phenomena in pattern formation,  International Conference on Differential Equations, Vol. 1, eds. B. Fiedler, K. Gröger, J. Spiekels, World Scientific, 1305-1307.
A. Doelman, V. Rottschäfer (1998) Multi-bump patterns near a
co-dimension 2 point, Tohoku Mathematical Publications,  Nr 8,  43-54.

Other publications

V. Rottschäfer (2014) SingulariteitenNieuw Archief van de Wiskunde 5/15 nr.4, 283 - 284.
A. Doelman, V. Rottschäfer, L. Sewalt, H. E. de Swart, A. Zagaris, J. Zijlstra  (2013) De complexe dynamica van fytoplanktonNieuw Archief van de Wiskunde 5/14 nr.3, 190 - 194.
Vivi Rottschäfer (2003) Wiskunde voor de rozenkweker, Nieuwe wiskrant23e jaargang,  nr. 3,
pp. 37 - 41.
Vivi Rottschäfer (2003) The 45th European Study Group Mathematics with Industry in Leiden,   ECMI newsletter 34, pp. 18 - 19.
Carina Edwards, Nick Ovenden , Vivi Rottschäfer (2003) Some cracking ideas on egg incubation, Proceedings 46th Eur. Study Group Ind., also see the ECMI newsletter 34 p. 21-24 for a shortened version.
Nick Ovenden, Vivi Rottschäfer (2002)  A greenhouse growth model for unselfish roses, Nieuw Archief voor Wiskunde, 5/3.


L. Sewalt, A. Doelman, H. Meijer (2014), V. Rottschäfer, A. Zagaris (2014), Tracking pattern evolution
through extended center manifold reduction and singular perturbations, submitted
Vivi Rottschäfer, Corine Meerman, Paul Zegeling (2013) Blowup solutions of the Korteweg-de
Vries equation, preprint Leiden 2013-26, submitted.