pde2path

Publication list, as of February 2026. See also here (possibly more up-to-date)

Note: The linked preprints may differ slightly from the published versions.
Books

Numerical continuation and bifurcation in Nonlinear PDEs, SIAM, 2021, SIAM
Nonlinear PDEs: A Dynamical Systems Approach, AMS, Graduate Studies in Mathematics 182, 2017, with Guido Schneider. AMS

Preprints

1. Electrolyte flows under magnetic fields: Manning-like counterion condensation in one dimension, Preprint 2026 (with Y. Tsori) preprint
2. Localised dynamic patterns in the complex cubic-quintic Swift-Hohenberg equation in one and two dimensions, Preprint 2026 (with E. Knobloch and N. Verschueren)preprint

Publications in journals and book chapters
2026-

3. Helfrich cylinders - instabilities, bifurcations, and amplitude equations, SIADS 2026 (with A.Meiners) preprint

2021-2025

4. Vegetation pattern formation and community assembly under drying climate trends (with M. Ferre, I. Pavithran, B. Bera, and E. Meron), Chaos, 35, 2025, preprint
5. Travelling vegetation-herbivore waves can sustain ecosystems threatened by droughts and population growth, Physica D, 2025, (with J. Singha and E.Meron),preprint
6. Phase transition and minimal interfaces on manifolds with conical singularities, (with D.Grieser, S.Held and B.Vertman), Nonlinearity, 2025 preprint
7. Breathers and mixed oscillatory states near a Turing-Hopf instability in a two-component reaction-diffusion system, (with F.Al Saadi, E.Knobloch and A.Meiners),Physica D, 2025, preprint
8. Numerical continuation and bifurcation for differential geometric PDEs, NMTMA, OA-2024-0005, 2024, (with A. Meiners), preprint
9. Time-dependent localised patterns in a predator-prey model, Chaos, 34 (with F. Al Saadi, E. Knobloch and M. Nelson), 2024, preprint
10. Origin of Jumping Oscillons in an Excitable Reaction-Diffusion System PRE E, 2021, (with E. Knobloch and A. Yochelis), preprint
11. Nonlinear dynamics of modulated waves on graphene like quantum graphs, 2021, (with S. Gilg and G. Schneider), preprint
12. Numerical continuation and bifurcation in Nonlinear PDEs - Algorithms, Applications, and Experiments, Annual Report of the DMV, 2021.
13. Localized and extended patterns in the cubic-quintic Swift-Hohenberg equation on a disk, Phys. Rev. E, 104:014208, 2021, (with N. Verschueren and E.Knobloch) preprint
14. Optimal spatial patterns in feeding, fishing, and pollution, DCDS-S, 2021, preprint
15. Optimal Stock-Enhancement of a Spatially Distributed Renewable Resource, Journal of Economic Dynamics & Control, 123, 104060, 2021 (with Th. Upmann, L. Hammann, B. Blasius). preprint

2016-2020

16. Bending and pinching of three-phase stripes: From secondary instabilities to morphological deformations in organic photovoltaics, Phys. Rev. E, 102, 062213, 2020 (with A. Shapira, N. Gavish and A. Yochelis)
17. Stripes on finite domains: Why the zigzag instability is only a partial story, Chaos, 30, 073104, 2020 (with A. Shapira and A. Yochelis) preprint
18. The role of spatial self-organisation in the design of agroforestry system, PLOS ONE, 15:7, e0236325, 2020 (with O. Tzuk and E. Meron) preprint
19. Snaking branches of planar BCC fronts in the 3D Brusselator, Physica D, 406, 132383, 2020, (with D. Wetzel) preprint
20. Defect-like structures and localised patterns in the cubic-quintic-septic Swift-Hohenberg equation, PRE, 100:1, 012204, 2019, with E. Knobloch and D. Wetzel) preprint
21. Optimal fishery with Coastal Catch, Natural Resource Modelling, e12235, 2019 (with D. Grass and Th. Upmann) preprint
22. Continuation for thin film hydrodynamics and related scalar problems, in Comput. Methods Appl. Sci, 50, Springer, Cham, 2019 (with S. Engelnkemper, S. V. Gurevich, D. Wetzel and U. Thiele), preprint.
23. Hopf bifurcation and time periodic orbits with pde2path - algorithms and applications, Comm. in Comp. Phys., 2019, preprint, pde2path homepage.

(This replaces the old version (2016), where the algorithms, applications, and implementations were reviewed in a single document. Now the paper focusses on the algorithms and applications, while the implementation is reviewed in a Tutorial on Hopf bifurcation; see also pde2path tutorials.

24. Mean field approach to first and second order phase transitions in ionic liquids, PRE, 95:060201, 2017, preprint, (with S. Bier, N. Gavish and A. Yochelis)
25. Desertification by Front Propagation?, Journal of Theoretical Biology 418 (2017), 27-35, (with Y. Zelnik, U. Feudel and E. Meron) preprint
26. Optimal management and spatial patterns in a distributed shallow lake model, 1:1-21, 2017, (with D. Grass), preprint
27. Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media, Asymptotic Analysis, 99 (1-2), pp. 53-65, 2016 (with K. Matthies), preprint
28. Sine-Gordon solitons in networks: Scattering and transmission at vertices, Europ. Phys. Letters 115: 50002, 2016 (with Z. Sobirov, D. Babajanov, K. Nakamura and D. Matrasulov), preprint
29. Optimal control and spatial patterns in a semi-arid vegetation system, Natural Resource Modelling, 29:2, 229-258, 2016, preprint
30. Bifurcation of Nonlinear Bloch Waves from the Spectrum in the Gross-Pitaevskii Equation, Journal of Nonlinear Science, 26:3, 581-618, 2016, (with T. Dohnal), preprint

2011-2015

31. Exact solutions of the Cauchy problem for the linearised KdV equation on metric star graphs, Uzbek Mathematical J, 2015:3, 143-154, (with Z. Sobirov and M. Akhmedov), preprint
32. Soliton transport in tubular networks: transmission at vertices in the shrinking limit, PRE 91, 023209, 2015, (with D. Grieser, Z. Sobirov, D. Babajanov and D. Matrasulov), preprint
33. Individual-based model for quorum sensing with background flow, Bull. Math. Biology, (with J. Müller and B. Hense), 2014, preprint
34. Numerical results for snaking of patterns over patterns in some 2D Selkov-Schnakenberg Reaction-Diffusion systems, SIADS, 13-1:94-128, 2014 (with D. Wetzel) preprint,
35. pde2path - a Matlab package for continuation and bifurcation in 2D elliptic systems, NMTMA (Numerical Mathematics: Theory, Methods and Applications), 7:58-106, 2014 (with D. Wetzel and J. Rademacher) preprint, pde2path homepage
36. Approximating the dynamics of communicating cells in a diffusive medium by ODEs -Â Homogenization with Localization, J. Math. Biology, 2012, (with J. Müller) preprint
37. Diffusive stability and diffusive mixing of periodic wave trains in reaction diffusion systems. JDE, 252, 3541-3574, 2012, (with B. Sandstede, A. Scheel and G. Schneider) preprint
38. Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms, EJDE, 2012:61, 1-51, 2012, (with T. Häcker and G. Schneider) preprint
39. Travelling interface modulations in the NH₃+O₂ reaction on a Rh(110) surface, Physical Chemistry Chemical Physics, 14, 5260-5264, 2012, (with M. Rafti, F. Lovis, V. Krupennikova and R. Imbihl) preprint
40. Corrigendum to 38, Proc. Royal Soc. Edinburgh, 141A, 819-824, 2011 (with R. Kaiser), preprint
41. Interfacing Fortran routines from Matlab in a simple and efficient way - with applications to ordinary and partial differential equations Summer School Modern Computational Science, Oldenburg 2011, Universitätsverlag Oldenburg, 2011, preprint,
42. Local existence and uniqueness of solutions of the weak electrolyte model describing electro-convection in nematic liquid crystals. ZAMM, 91:3, 247-256, 2011 (with W.-P. Düll and G. Schneider) preprint
43. Erratum to (published version of) 42, Physica D, 240, 357-362, 2011 (with T. Dohnal)preprint
44. Interaction of modulated pulses in nonlinear oscillator chains, J. Diff. Eq. Appl., 17:3, 279-298, 2011 (with G. Schneider and M. Wand) preprint

2006-2010

45. Amplitude equations - an invitation to multiple scale analysis Summer School Modern Computational Science, Oldenburg 2010, Universitätsverlag Oldenburg, 2010, preprint,
46. Statistics for surface modes of nanoparticles with shape fluctuations, Commun. in Comp. Physics, 8, 1224, 2010, (with F. Rüting), preprint,
47. Well-posedness of some initial-boundary-value problems for dynamo-generated poloidal magnetic fields, Proc. Royal Soc. Edinburgh, 139A, 1209-1235, 2009 (with R. Kaiser) preprint
48. Perturbation theory for plasmonic eigenvalues, Phys. Rev. B, 80:245405, 2009, (with D. Grieser, S. Biehs, O. Huth, F. Rüting, and M. Holthaus) preprint
49. An integral boundary layer equation for film flow over inclined wavy bottoms, Phys. of Fluids, 21, 092105, 2009. (with T. Häcker) preprint
50. A short ad hoc introduction to spectral methods for parabolic PDE and the Navier-Stokes equations, in Summer School Modern Computational Science, Oldenburg 2009, Universitätsverlag Oldenburg, 2009 preprint, software
51. Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevsky equation with a non-separable periodic potential, Physica D, 238: 860-879, 2009. (with T. Dohnal) (updated version)
52. Linear resonance in viscous films on inclined planes. IJ Mutiphase Flow 34: 580-589, 2008. (with A. Wierschem, V. Bontozoglou, C. Heining, and N. Aksel)
53. A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in ℝ³, Comm. PDE 33:5, 772-783, 2008. (with A. Melcher and G. Schneider) preprint
54. A remark about the justification of the nonlinear Schrödinger equation in quadratic spatially periodic media, ZAMP, 59:1-4, 2008 (with C. Blank, M. Chirilus-Bruckner, C. Chong, V. Lescarret and G. Schneider) preprint
55. Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves, Math. Anal. Appl. 347, 304Â314 (2008), (with M. Chirilus-Bruckner, C. Chong, and G. Schneider) preprint
56. Mass transport of alkali metal with pulses in a surface reaction, Phys. Rev. E, 78:055203(R), 2008, (with M. Hinz, R. Imbihl, Y. Keverekidis, and Q. Liang) preprint
57. Long time persistence of KdV solitons as transient dynamics in a model of inclined film flow, Proc. Roy. Soc. Edinb., 137A: 133-146, 2007 (with R.L. Pego and G. Schneider) preprint
58. Exponential averaging and travelling waves in rapidly varying periodic media, Mathematische Nachrichten, 280:4, 408-422, 2007 (with K. Matthies and G. Schneider) preprint
59. Self-similar decay of localised perturbations of the Nusselt solution for the Navier-Stokes equations on an inclined plane, Arch.Rat.Mech.Anal. 184:3, 401-447, 2007 preprint
60. The amplitude equations for the first instability of electro-convection in nematic liquid crystals in case of two unbounded space directions, Nonlinearity 20:1361-1386, 2007. (with G. Schneider) preprint
61. On the interaction of modulating pulses with different carrier waves, Mathematical Methods Applied Sciences, 30:15, 1965-1978, 2007. (with M. Chirilus-Bruckner and G. Schneider) preprint
62. The mathematics of light pulses in dispersive media, Jahresberichte der DMV, 109:3, 139-161, 2007 (with G. Schneider) preprint
63. A spatially periodic Kuramoto-Sivashinsky equation as a model problem for inclined film flow over wavy bottom. EJDE 118, 1-18, 2007, (with A. Wierschem) preprint
64. Simulation of the life cycle of adsorbate islands on the Pt(100) surface during the NO+NH₃ reaction. Chem. Phys. Letters, 421:4-6, 577-583. 2006. (with M. Rafti, J. L. Vicente and R. Imbihl) preprint
65. Justification of the Nonlinear Schrödinger equation in spatially periodic media, ZAMP, 57:6, 905-939, 2006 (with K. Busch, G. Schneider and L. Tkeshelashvili) preprint

2001-2005

66. Pattern formation for NO+NH₃ on Pt(100) - 2-dimensional numerical results, Phys. Rev.E, 71, 016207, 2005. preprint
67. Standing waves, clustering, and phase waves in 1d-simulations of kinetic relaxation oscillations in NO+NH₃ on Pt(100) coupled by diffusion. Physica D 190:249-265, 2004. preprint
68. Stable transport of information near essentially unstable localised structures. Discrete Contin.Dyn.Syst.B 4:2, 349-390, 2004. (with Th. Gallay and G. Schneider) preprint
69. Relaxed plasma vacuum states in cylinders. Q.J. Mech. Appl. Math., 57:1, 1-17, 2004 (with R. Kaiser) preprint
70. Self-similar decay of localised perturbations in the Integral Boundary Layer equation. Journal Diff. Eq, 207:2, 407-422, 2004.preprint
71. Validity of the Ginzburg-Landau approximation in pattern forming systems with time periodic forcing. Dynamics and Bifurcations of Patterns in Dissipative Systems, World Scientific, 39-57, 2004. (with N. Breindl and G. Schneider) preprint
72. Existence and stability of modulating pulse solutions in Maxwell's equations describing nonlinear optics. ZAMP 54, 677-712, 2003. (with G. Schneider) preprint
73. Approximation of the Integral Boundary Layer equation by the Kuramoto-Sivashinsky equation. SIAM J. Appl. Math. 63:4, 1359-1377, 2003. preprint
74. Almost global existence and transient self similar decay for Poiseuille flow at criticality over exponentially long times. Physica D 185:3-4, 209-226, 2003 (with G. Schneider) preprint
75. Adiabatic reduction and hysteresis of the LFI-model of NO+NH₃ on Pt(100). Chem. Phys. Let., 382, 232-244, 2003 (with R. Imbihl, M. Rafti, I.M. Iruzun, J.L. Vicente and E.E. Mola) preprint
76. Stability and diffusive dynamics on unbounded domains. In Ergodic Theory, Analysis and Efficient Simulation of Dynamical Systems, ed. B. Fiedler, Springer, 563-584, 2001. (with A. Mielke and G. Schneider)preprint
77. Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Asymptot. Anal. 28:2, 163-180, 2001. (with G. Schneider) preprint
78. Stable modulating multi-pulse solutions for dissipative systems with resonant spatially periodic forcing. J. Nonlin. Sci.,11:2, 89-121, 2001. preprint
79. Diffusive stability of rolls in the two-dimensional real and complex Swift-Hohenberg equation. Comm. PDE 24:11&12, 2109-2146, 1999.preprint

Conference papers

80. pde2path - V2 : multi-parameter continuation and periodic domains, 2014, in H. Ecker, A. Steindl, S. Jakubek, eds, ENOC 2014 - Proceedings of 8th European Nonlinear Dynamics Conference, ISBN: 978-3-200-03433-4. (with T. Dohnal, J. Rademacher and D. Wetzel), preprint, pde2path homepage
81. Modelling of film flows over inclined wavy bottoms, PAMM 8:10721-10722, 2009 (with T. Häcker)
82. Resonance in viscous film flow over topography PAMM 7:4100025-4100026, 2008 (with C. Heining, A. Wierschem, V. Bontozoglou and N. Aksel)
83. Mathematical theory for the Ginzburg-Landau approximation in pattern forming systems with time-periodic forcing - with applications to electro-convection in nematic liquid crystals. Proceedings ofEqua∂iff-11: 507-517, 2005. (with N. Breindl and G. Schneider) preprint
84. Local in time nonlinear stability of pulses in an unstable medium. XIV^th International Congress on Mathematical Physics, Lisboa 2003, 296-303, World Scientific, 2005. (with R.L. Pego and G. Schneider)
85. Rolls and modulating pulses in Swift-Hohenberg type of equations, in International Conference on Differential Equations, Equadiff 99, World Scientific, 408-413, 2000.

Qualification work

• Stability investigations in a model for shape memory alloys, Diplom thesis, University of Hannover, 1996. Published as Preprint A3 of the series Stress and distortion related phase transitions in engineering materials, research project of the VW foundation: I 70 284. pdf
• Rollers and modulating multipulses in pattern-forming systems, dissertation, University of Bayreuth, 2000. (see 70, 69)
• Qualitative Theorie nichtlinear partielle Differentialgleichungen der Mathematischen Physik, Habilitationsschrift, Universität Karlsruhe, 2004. (cumulative, see 68-56, 49)