Journal Articles

• S. van der Stelt, A. Doelman, G.M. Hek , J. Rademacher (2011), `Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model', pdf file.
• M. Holzer, A. Doelman, T.J. Kaper (2011), `Existence and stability of traveling pulses in a reaction-diffusion-mechanics system', submitted, pdf file.
• G. Derks, A. Doelman, C.J.K. Knight, H. Susanto (2010) `Pinned fluxons in a Josephson junction with a finite-length inhomogeneity', to appear in Eur. J. Appl. Math., pdf file.
• A. Zagaris, A. Doelman (2010) `Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model', to appear in Nonlinearity, pdf file preprint.
• A. Doelman, J. Rademacher, S. van der Stelt (2012) `Hopf dances near the tips of Busse balloons', Discr. Cont. Dyn. Syst. (S) 5(1) 61-92, pdf file preprint.
• P.J.A. van Heijster, A. Doelman, T.J. Kaper, Y. Nishiura, K.-I. Ueda (2011) `Pinned fronts in heterogeneous media of jump type', Nonlinearity 24 127-157.
• P.J.A. van Heijster, A. Doelman, T.J. Kaper, K. Promislow (2010) `Front interactions in a three-component system', SIAM J. Appl. Dyn. Syst. 9 (2) 292-332.
• A. Doelman, B. Sandstede , A. Scheel , G. Schneider (2009) `The dynamics of modulated wave trains', Memoirs of the AMS 199 (934).
• A. Zagaris , A. Doelman, N. N. Pham Thi, B. Sommeijer (2009) `Blooming in a non-local, coupled phytoplankton-nutrient model', SIAM J. Appl. Math, 69 (4) 3335-3368.
• J. Hazewinkel , S.B. Dalziel , A. Doelman, L.R.M. Maas (2008) `Tracer transport by internal wave beams', submitted.
• A. Doelman, P.J.A. van Heijster , T.J. Kaper (2009) `Pulse dynamics in a three-component system: existence analysis', J. Dyn. Diff. Eq., 21 (1) 73-115.
• P.J.A. van Heijster , A. Doelman, T.J. Kaper (2008) `Pulse dynamics in a three-component system: stability and bifurcations', Physica D, 237 (24) 3335-3368.
• A. Doelman, T.J. Kaper , K. Promislow (2007) `Nonlinear asymptotic stability of the semi-strong pulse dynamics in a regularized Gierer-Meinhardt model', SIAM J. Math. An., 38 (6) 1760-1787.
• G. Derks , A. Doelman, S.A. van Gils , H. Susanto (2007) `Stability analysis of $\pi$-kinks in a $0-\pi$ Josephson junction', SIAM J. Appl. Dyn. Syst., 6 (1) 99 - 141.
• A. Doelman, G.M. Hek , N.J.M. Valkhoff (2007) `Algebraically decaying pulses in a Ginzburg-Landau system with a neutrally stable mode', Nonlinearity , 20 357 - 389.
• A. Doelman, T.J. Kaper , L.A. Peletier (2006) `Homoclinic bifurcations at the onset of pulse self-replication', J. Differential Equations 231 359 - 423.
• M.A. Beck , A. Doelman, T.J. Kaper (2006) `A geometric construction of traveling waves in a bioremediation model', J. Nonl. Sc. 16 (4) 329 - 349.
• H. van der Ploeg , A. Doelman (2005) `Stability of spatially periodic pulse patterns in a class of singularly perturbed reaction-diffusion equations', Indiana Univ. Math. J. 54 (5) 1219 - 1301.
• G. M. Terra , A. Doelman, L.R.M. Maas (2004) `Weakly nonlinear cubic interactions in coastal resonance', J. Fluid Mech. 520 93 - 134.
• H. Susanto , S.A. van Gils , A. Doelman, G. Derks (2004) `Analysis of the stability of Josephson vortices at tricrystal boundaries: a 3 phi_0/2 case', Phys. Rev. B 69 212503.
• A. Doelman, G.M. Hek , N.J.M. Valkhoff (2004) `Stabilization by slow diffusion in a real Ginzburg-Landau system', J. Nonl. Sc. 14 237 - 278.
• A. Doelman, D. Iron , Y. Nishiura (2004) `Destabilization of fronts in a class of bi-stable systems', SIAM J. Math. An. 35 (6) 1420 - 1450.
• G. Derks , A. Doelman, S.A. van Gils , T.P.P. Visser (2003) `Travelling waves in a singularly perturbed sine-Gordon equation', Physica D 180 (1-2) 40 - 70.
• A. Doelman, T.J. Kaper (2003) `Semi-strong pulse interactions in a class of coupled reaction-diffusion equations', SIAM J. Appl. Dyn. Syst. 2 (1) 53 - 96.
• A. Doelman, B. Sandstede , A. Scheel , G. Schneider (2003) `Propagation of hexagonal patterns near onset', Eur. J. Appl. Math. 14 85 - 110.
• A. Doelman, H. van der Ploeg (2002) `Homoclinic stripe patterns', SIAM J. Appl. Dyn. Syst. 1 (1) 65 - 104.
• A. Doelman, A.F. Koenderink, L.R.M. Maas (2002) `Quasi-periodically forced nonlinear Helmholtz oscillators', Physica D 164 (1-2) 1 - 27.
• L.R.M. Maas , A. Doelman (2002) `Chaotic tides', J. Phys. Oceanogr. 32 (3) 870 - 890.
• A. Doelman, R. A. Gardner , T.J. Kaper (2002) `A stability index analysis of 1-D patterns of the Gray-Scott model', Memoirs of the AMS 155 (737).
• A. Doelman, T.J. Kaper , H. van der Ploeg (2001) `Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer-Meinhardt equation', Meth. Appl. Anal. 8 (2) 387 - 414.
• A. Doelman, R. A. Gardner , T.J. Kaper (2001) `Large stable pulse solutions in reaction-diffusion equations', Indiana Univ. Math. J. 50 (1) 443 - 507.
• A. Doelman, W. Eckhaus, T.J. Kaper (2001) `Slowly-modulated two-pulse solutions in the Gray-Scott model II: geometric theory, bifurcations and splitting dynamics', SIAM J. Appl. Math. , 61 (6) 2036 - 2062.
• A. Doelman, W. Eckhaus, T.J. Kaper (2000) `Slowly-modulated two-pulse solutions in the Gray-Scott model I: asymptotic construction and stability', SIAM J. Appl. Math. 61 (3) 1080 - 1102.
• D.S. Morgan , A. Doelman, T.J. Kaper (2000) `Stationary periodic patterns in the 1D Gray-Scott model', Meth. Appl. Anal. 7 (1) 105-150.
• A. Doelman, G.M. Hek (2000) `Homoclinic saddle-node bifurcations in singularly perturbed systems', J. Dyn. Diff. Eq. 12 (1) 169-216.
• G.M. Hek , A. Doelman, P. Holmes (1998) `Homoclinic saddle-node bifurcations and subshifts in a three-dimensional flow', Arch. Rat. Mech. An. 145 291-329.
• R. Schielen, A. Doelman (1998) `Modulation equations for spatially periodic systems: derivation and solutions', SIAM J. Appl. Math. 58 (6) 1901-1930.
• A. Doelman, R. A. Gardner , T.J. Kaper (1998) `Stability analysis of singular patterns in the 1-D Gray-Scott model: A matched asymptotics approach', Physica D 122 1-36.
• V. Rottschäfer , A. Doelman (1998) `On the transition of the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation', Physica D 118 261-292.
• A. Doelman, V. Rottschäfer (1997) `Singularly perturbed and non-local modulation equations for systems with interacting instability mechanisms', J. Nonl. Sc. 7 371-409.
• A. Doelman, T.J. Kaper , P.A. Zegeling (1997) `Pattern formation in the 1-D Gray-Scott model', Nonlinearity 10 523-563.
• A. Doelman (1996) `Breaking the hidden symmetry in the Ginzburg-Landau equation' Physica D 97 398-428.
• P. Takac , P. Bollerman, A. Doelman, A. van Harten , E.S. Titi (1996) `Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation', SIAM J. Math. An. 27 (2) 424 - 448.
• A. Doelman, P. Holmes (1996) `Errata: Homoclinic explosions and implosions', Phil. Trans. Roy. Soc. Lond. A 354 1837-1839.
• A. Doelman, P. Holmes (1996) `Homoclinic explosions and implosions', Phil. Trans. Roy. Soc. Lond. A 354 845-893.
• A. Doelman, R. A. Gardner , C.K.R.T. Jones (1995) `Instability of quasiperiodic solutions of the Ginzburg-Landau equation' Proc. Roy. Soc. Edinb. 125A 501-517.
• A. Doelman, F. Verhulst (1994) `Bifurcations of strongly nonlinear self-exited oscillations' Math. Meth. Appl. Sc. 17 189-207.
• A. Doelman, E.S. Titi (1993) `Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation' Numer. Funct. Anal. and Opt. 14 299-321.
• R. Schielen, A. Doelman, Thesis H.E. de Swart (1993) `On the nonlinear dynamics of free bars in straight channels' J. Fluid Mech. 252 325-356.
• A. Doelman (1993) `Traveling waves in the complex Ginzburg-Landau equation' J. Nonl. Sc. 3 225-266.
• A. Doelman, W. Eckhaus (1991) `Periodic and quasi-periodic solutions of degenerate modulation equations', Physica D 53 249-266.
• A. Doelman (1991) `Finite dimensional models of the Ginzburg-Landau equation', Nonlinearity 4 231-250.
• A. Doelman (1989) `Slow time-periodic solutions of the Ginzburg-Landau equation', Physica D 40 156-172.

Books

• A. Doelman, A. van Harten (eds.) (1995) `Nonlinear Dynamics and Pattern Formation in the Natural Environment' , Longman, UK; Pitman Research Notes in Mathematics 335 .

Contributions to Books and Conference Proceedings

• J. Hazewinkel , P. van Breevoort, A. Doelman, L.R.M. Maas , S.B. Dalziel (2007) `Equilibrium spectrum for internal wave attractors in a trapezoidal basin', in Proceedings of the 5th International Symposium on Environmental Hydraulics.
• G.M. Hek, N. Valkhoff, A. Doelman (2005) `Stabilization of pulses by competing instability mechanisms', pp 2353-2361 in Proceedings ENOC-2005, Eindhoven, Netherlands.
• A. Doelman, D. Iron, Y. Nishiura (2005) `Edge bifurcations in singularly perturbed reaction-diffusion equations: a case study', pp 783-788 in `EQUADIFF03 International Conference on Differential Equations', (F. Dumortier, H. Broer, J. Mahwin, A. Vanderbauwhede, S. Verduyn Lunel eds.), World Scientific, Singapore etc.
• A. Doelman (2002) `Stabilization of pulses by diffusion', contribution to the Biennial Report 2000-2001 of the Stieltjes Institute for Mathematics, postscript file.
• P. Holmes, A. Doelman, G.M. Hek, G. Domokos (2001) `Homoclinic orbits and chaos in three- and four-dimensional flows', paper for Royal Society Discussion Meeting on Topological Methods in the Physical Sciences , London, Nov 15-16, 2000, Phil. Trans. Roy. Soc. Lond. A 359 1429-1438.
• A. Doelman, W. Eckhaus, T.J. Kaper (2000) `A note on two pulse solutions in the $1$-D Gray-Scott model', pp 775-780 in `EQUADIFF99, International Conference on Differential Equations' 2 Vol., (B. Fiedler, K. Gröger, J. Sprekels eds.), World Scientific, Singapore etc.
• A. Doelman, R.A. Gardner, T.J. Kaper (2000) `The stability of large pulse solutions in the generalized Gierer-Meinhardt equation', pp 781-786 in `EQUADIFF99, International Conference on Differential Equations' 2 Vol., (B. Fiedler, K. Gröger, J. Sprekels eds.), World Scientific, Singapore etc.
• A. Doelman, V. Rottschafer (1998) `Multi-bump patterns near a co-dimension 2 point', Proc. `Asymptotics in Nonlinear Diffusive Systems', Sendai, Japan, Tohoku Math. Pub., 8 43-54.
• A. Doelman, P. Holmes (1995) `On the creation of multi-pulse traveling waves by global bifurcations' pp. 201-208 in `Structure and Dynamics of Nonlinear Waves in Fluids' (A. Mielke & K. Kirchgässner eds.), World Scientific, Singapore etc. Advanced Series in Nonlinear Dynamics 7.
• A. Doelman, W. Eckhaus, R. Kuske, R. Schielen (1995) `Pattern formation in systems on spatially periodic domains' pp. 85-105 in `Nonlinear Dynamics and Pattern Formation in the Natural Environment' (A. Doelman, A. van Harten (eds.)), Longman, UK; Pitman Research Notes in Mathematics 335 .
• A. Doelman (1993) `Travelling, non-periodic patterns in nonlinear stability problems' Proc. Fourth European Turbulence Conference, Delft, the Netherlands 1992 (F.T.M. Nieuwstadt ed.), Appl. Sc. Res. 51 37-42.
• A. Doelman, E.S. Titi (1993) `Exponential convergence of the Galerkin approximation for the Ginzburg-Landau equation' pp 241-252 in `Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters', (H.G. Kaper, M. Garbey eds.), Kluwer Academic Publishers, Dordrecht.
• A. Doelman, W. Eckhaus (1991) `Quasi-periodic and homoclinic solutions of modulation equations', Proc. IUTAM-Symp. on Nonlinear Hydrodynamic Stability and Transition, Sophia-Antipolis France 1990 (G. Iooss ed.), Europ. J. Mech. B/Fluids 10 131-136.
• A. Doelman, J. Grasman (1988) `Low order spectral methods in hydrodynamics', pp 86-97 in `Trends in Applications of Mathematics to Mechanics , (J.F. Besseling, W. Eckhaus eds.), Springer-Verlag, Berlin etc.

Publications in Dutch

• A. Doelman `De dynamica van patronen: wiskunde en woestijnen', Vakantiecursus 2007 Wiskunde in Beweging, CWI syllabus 57 27-45 (2007).
• A. Doelman `Het begrip dimensie: theorie en experiment', Vakantiecursus 2001 Experimentele wiskunde, CWI syllabus 49 17-38 en Nieuw Archief van de Wiskunde 5/4 (2) 151-160 (2003).
• A. Doelman, H. Duistermaat, J. Grasman, A. van Harten, `In Memorian Wiktor Eckhaus', Nieuw Archief van de Wiskunde 5/2 (2) 18-20 (2001) en ITW Nieuws 11 (1) 10-13 (2001).
• A. Doelman (2000), `Patronen en Golven' , rede uitgesproken bij de aanvaarding van het ambt van hoogleraar in de Wiskunde, 27 oktober 1999, oratiereeks Vossiuspers AUP; ook als Nieuw Archief van de Wiskunde 5/1 (1) 18-27 (2000).
• A. Doelman (1999) `Toegepaste Analyse en Dynamische Systemen' Nieuwsbrief KdV Inst. april 9-13.
• A. Doelman (1996) `Patroonvorming in reactie-diffusie systemen' De Vakidioot 2 2-6.

Thesis

• A. Doelman (1990) `On the Nonlinear Evolution of Patterns - Modulation Equations and Their Solutions' , Rijksuniversiteit Utrecht.

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