pde2path

Publikationsliste, Stand Oktober 2024. Siehe auch hier (eventuell aktueller)

Hinweis: Die verlinkten Preprints können leicht von den publizierten Versionen abweichen.
Bücher
 
Numerical continuation and bifurcation in Nonlinear PDEs, SIAM, 2021, SIAM
Nonlinear PDEs: A Dynamical Systems Approach, AMS, Graduate Studies in Mathematics 182, 2017, mit Guido Schneider. AMS

Preprints

1. Traveling vegetation-herbivore waves can sustain ecosystems threatened by droughts and population growth, 2024, (mit J. Singha and E.Meron),preprint
2. Breathers and mixed oscillatory states near a Turing-Hopf instability in a two-component reaction-diffusion system, 2024, (mit F.Al Saadi, E.Knobloch and A.Meiners),preprint
3. Phase transition and minimal interfaces on manifolds with conical singularities, 2024, (mit D.Grieser, S.Held and B.Vertman),preprint

Veröffentlichungen in Zeitschriften und Buchkapitel
2021–...

1. Numerical continuation and bifurcation for differential geometric PDEs, NMTMA, OA-2024-0005, 2024, (mit A. Meiners), preprint
2. Time-dependent localized patterns in a predator–prey model, Chaos, 34 (mit  F. Al Saadi, E. Knobloch and M. Nelson), 2024, preprint
3. Origin of Jumping Oscillons in an Excitable Reaction-Diffusion System PRE E, 2021, (mit E. Knobloch and A. Yochelis), preprint
4. Nonlinear dynamics of modulated waves on graphene like quantum graphs, 2021, (mit S. Gilg and G. Schneider), preprint
5. Numerical continuation and bifurcation in Nonlinear PDEs - Algorithms, Applications, and Experiments, Jahresbericht der DMV, 2021.
6. Localized and extended patterns in the cubic-quintic Swift-Hohenberg equation on a disk, Phys. Rev. E, 104:014208, 2021, (mit N. Verschueren und E.Knobloch) preprint
7. Optimal spatial patterns in feeding, fishing, and pollution, DCDS-S, 2021, preprint
8. Optimal Stock–Enhancement of a Spatially Distributed Renewable Resource, Journal of Economic Dynamics & Control, 123, 104060, 2021 (mit Th. Upmann, L. Hammann, B. Blasius). preprint

2016–2020

7. Bending and pinching of three-phase stripes: From secondary instabilities to morphological deformations in organic photovoltaics, Phys. Rev. E, 102, 062213, 2020 (mit A. Shapira, N. Gavish und A. Yochelis)
8. Stripes on finite domains: Why the zigzag instability is only a partial story, Chaos, 30, 073104, 2020 (mit A. Shapira und A. Yochelis) preprint
9. The role of spatial self-organization in the design of agroforestry system, PLOS ONE, 15:7, e0236325, 2020 (mit O. Tzuk und E. Meron) preprint
10. Snaking branches of planar BCC fronts in the 3D Brusselator, Physica D, 406, 132383, 2020, (mit D. Wetzel) preprint
11. Defect–like structures and localized patterns in the cubic–quintic–septic Swift–Hohenberg equation, PRE, 100:1, 012204, 2019, mit E. Knobloch und D. Wetzel) preprint
12. Optimal fishery with Coastal Catch, Natural Resource Modelling, e12235, 2019 (mit D. Grass und Th. Upmann) preprint
13. Continuation for thin film hydrodynamics and related scalar problems, in Comput. Methods Appl. Sci., 50, Springer, Cham, 2019 (mit S. Engelnkemper, S. V. Gurevich, D. Wetzel and U. Thiele), preprint.
14. 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.

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

2011–2015

22. Exact solutions of the Cauchy problem for the linearized KdV equation on metric star graphs, Uzbek Mathematical J, 2015:3, 143-154, (mit Z. Sobirov und M. Akhmedov), preprint
23. Soliton transport in tubular networks: transmission at vertices in the shrinking limit, PRE 91, 023209, 2015, (mit D. Grieser, Z. Sobirov, D. Babajanov and D. Matrasulov), preprint
24. Individual-based model for quorum sensing with background flow, Bull. Math. Biology, (mit J. Müller und B. Hense), 2014, preprint
25. Numerical results for snaking of patterns over patterns in some 2D Selkov–Schnakenberg Reaction–Diffusion systems, SIADS, 13-1:94–128, 2014 (mit D. Wetzel) preprint,
26. pde2path – a Matlab package for continuation and bifurcation in 2D elliptic systems, NMTMA (Numerical Mathematics: Theory, Methods and Applications), 7:58–106, 2014 (mit D. Wetzel und J. Rademacher) preprint, pde2path homepage
27. Approximating the dynamics of communicating cells in a diffusive medium by ODEs -Â Homogenization with Localization, J. Math. Biology, 2012, (mit J. Müller) preprint
28. Diffusive stability and diffusive mixing of periodic wave trains in reaction diffusion systems. JDE, 252, 3541–3574, 2012. (mit B. Sandstede, A. Scheel and G. Schneider) preprint
29. 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, (mit T. Häcker und G. Schneider) preprint
30. Traveling interface modulations in the NH₃+O₂ reaction on a Rh(110) surface, Physical Chemistry Chemical Physics, 14, 5260–5264, 2012, (mit M. Rafti, F. Lovis, V. Krupennikova and R. Imbihl) preprint
31. Corrigendum to 38, Proc. Royal Soc. Edinburgh, 141A, 819-824, 2011 (mit R. Kaiser), preprint
32. 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,
33. Local existence and uniqueness of solutions of the weak electrolyte model describing electro-convection in nematic liquid crystals. ZAMM, 91:3, 247-256, 2011 (mit W.-P. Düll und G. Schneider) preprint
34. Erratum to (published version of) 42, Physica D, 240, 357-362, 2011 (mit T. Dohnal)preprint
35. Interaction of modulated pulses in nonlinear oscillator chains, J. Diff. Eq. Appl., 17:3, 279-298, 2011 (mit G. Schneider und M. Wand) preprint

2006-2010

36. Amplitude equations – an invitation to multiple scale analysis Summer School Modern Computational Science, Oldenburg 2010, Universitätsverlag Oldenburg, 2010, preprint,
37. Statistics for surface modes of nanoparticles with shape fluctuations, Commun. in Comp. Physics, 8, 1224, 2010, (mit F. Rüting), preprint,
38. Well-posedness of some initial-boundary-value problems for dynamo-generated poloidal magnetic fields, Proc. Royal Soc. Edinburgh, 139A, 1209-1235, 2009 (mit R. Kaiser) preprint
39. Perturbation theory for plasmonic eigenvalues, Phys. Rev. B, 80:245405, 2009, (mit D. Grieser, S. Biehs, O. Huth, F. Rüting, and M. Holthaus) preprint
40. An integral boundary layer equation for film flow over inclined wavy bottoms, Phys. of Fluids, 21, 092105, 2009. (mit T. Häcker) preprint
41. 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
42. Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevsky equation with a non-separable periodic potential, Physica D, 238: 860-879, 2009. (mit T. Dohnal) (updated version)
43. Linear Resonance in viscous films on inclined planes. IJ Mutiphase Flow 34: 580–589, 2008. (mit A. Wierschem, V. Bontozoglou, C. Heining, und N. Aksel)
44. A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in ℝ³, Comm. PDE 33:5, 772–783, 2008. (mit A. Melcher and G. Schneider) preprint
45. A remark about the justification of the nonlinear Schrödinger equation in quadratic spatially periodic media, ZAMP, 59:1-4, 2008 (mit C. Blank, M. Chirilus-Bruckner, C. Chong, V. Lescarret and G. Schneider) preprint
46. Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves, Math. Anal. Appl. 347, 304Â314 (2008), (mit M. Chirilus-Bruckner, C. Chong, and G. Schneider) preprint
47. Mass transport of alkali metal with pulses in a surface reaction, Phys. Rev. E, 78:055203(R), 2008, (mit M. Hinz, R. Imbihl, Y. Keverekidis und Q. Liang) preprint
48. Long time persistence of KdV solitons as transient dynamics in a model of inclined film flow, Proc. Roy. Soc. Edinb., 137A: 133–146, 2007. (mit R.L. Pego and G. Schneider) preprint
49. Exponential averaging and traveling waves in rapidly varying periodic media, Mathematische Nachrichten, 280:4, 408-422, 2007 (mit K. Matthies and G. Schneider) preprint
50. Self–similar decay of localized perturbations of the Nusselt solution for the Navier–Stokes equations on an inclined plane, Arch.Rat.Mech.Anal. 184:3, 401–447, 2007 preprint
51. 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. (mit G. Schneider) preprint
52. On the interaction of modulating pulses with different carrier waves, Mathematical Methods Applied Sciences, 30:15, 1965–1978, 2007. (mit M. Chirilus-Bruckner und G. Schneider) preprint
53. The mathematics of light pulses in dispersive media, Jahresberichte der DMV, 109:3, 139-161, 2007 (mit G. Schneider) preprint
54. A spatially periodic Kuramoto-Sivashinsky equation as a model problem for inclined film flow over wavy bottom. EJDE 118, 1-18, 2007, (mit A. Wierschem) preprint
55. 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. (mit M. Rafti, J. L. Vicente and R. Imbihl) preprint
56. Justification of the Nonlinear Schrödinger equation in spatially periodic media, ZAMP, 57:6, 905–939, 2006 (mit K. Busch, G. Schneider and L. Tkeshelashvili) preprint

2001-2005

57. Pattern formation for NO+NH₃ on Pt(100) – 2-dimensional numerical results, Phys. Rev.E, 71, 016207, 2005. preprint
58. 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
59. Stable transport of information near essentially unstable localized structures. Discrete Contin.Dyn.Syst.B 4:2, 349–390, 2004. (mit Th. Gallay und G. Schneider) preprint
60. Relaxed plasma vacuum states in cylinders. Q.J. Mech. Appl. Math., 57:1, 1–17, 2004. (mit R. Kaiser) preprint
61. Self–similar decay of localized perturbations in the Integral Boundary Layer equation. Journal Diff. Eq., 207:2, 407–422, 2004.preprint
62. 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. (mit N. Breindl und G. Schneider) preprint
63. Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. ZAMP 54, 677-712, 2003. (mit G. Schneider) preprint
64. Approximation of the Integral Boundary Layer equation by the Kuramoto–Sivashinsky equation. SIAM J. Appl. Math. 63:4, 1359–1377, 2003. preprint
65. 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. (mit G. Schneider) preprint
66. Adiabatic reduction and hysteresis of the LFI–model of NO+NH₃ on Pt(100). Chem. Phys. Let., 382, 232–244, 2003. (mit R. Imbihl, M. Rafti, I.M. Iruzun, J.L. Vicente und E.E. Mola) preprint
67. Stability and diffusive dynamics on unbounded domains. In Ergodic Theory, Analysis and Efficient Simulation of Dynamical Systems, ed. B. Fiedler, Springer, 563-584, 2001. (mit A. Mielke und G. Schneider)preprint
68. Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Asymptot. Anal. 28:2, 163-180, 2001. (mit G. Schneider) preprint
69. Stable modulating multi-pulse solutions for dissipative systems with resonant spatially periodic forcing. J. Nonlin. Sci.,11:2, 89-121, 2001. preprint
70. Diffusive stability of rolls in the two-dimensional real and complex Swift–Hohenberg equation. Comm. PDE 24:11&12, 2109-2146, 1999.preprint

Tagungsbeiträge

71. 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. (mit T. Dohnal, J. Rademacher und D. Wetzel), preprint, pde2path homepage
72. Modeling of film flows over inclined wavy bottoms, PAMM 8:10721-10722, 2009 (mit T. Häcker)
73. Resonance in viscous film flow over topography PAMM 7:4100025–4100026, 2008 (mit C. Heining, A. Wierschem, V. Bontozoglou und N. Aksel)
74. 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 of Equa∂iff–11: 507–517, 2005. (mit N. Breindl and G. Schneider) preprint
75. 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. (mit R.L. Pego und G. Schneider)
76. Rolls and modulating pulses in Swift–Hohenberg type of equations, in International Conference on Differential Equations, Equadiff 99, World Scientific, 408-413, 2000.

Qualifikationsarbeiten

• Stabilitätsuntersuchungen in einem Modell für Formgedächtnislegierungen, Diplomarbeit, Universität Hannover, 1996. Veröffentlicht als Preprint A3 der Reihe Spannungs– und Verzerrungsbedingte Phasenübergänge in Ingenieurswerkstoffen, Forschungsprojekt der VW–Stiftung: I 70 284. pdf
• Rollen und modulierende Multipulse in musterbildenden Systemen, Dissertation, Universität Bayreuth, 2000. (siehe 70, 69)
• Qualitative Theorie nichtlinearer partieller Differentialgleichungen der Mathematischen Physik, Habilitationsschrift, Universität Karlsruhe, 2004. (kumulativ, siehe 68–56, 49)