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Forschung/Veröffentlichungen

Forschung/Veröffentlichungen

pde2path

 

Publikationsliste, Stand 28. November 2021. Siehe auch hier (eventuell aktueller)


Hinweis: Die verlinkten Preprints können leicht von den publizierten Versionen abweichen.
Bücher
PIC PIC
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. Origin of Jumping Oscillons in an Excitable Reaction-Diffusion System 2021, (mit E. Knobloch and A. Yochelis), preprint
  2. Nonlinear dynamics of modulated waves on graphene like quantum graphs, 2021, (mit S. Gilg and G. Schneider), preprint

Veröffentlichungen in Zeitschriften und Buchkapitel
2021–...

  1. Numerical continuation and bifurcation in Nonlinear PDEs - Algorithms, Applications, and Experiments, Jahresbericht der DMV, 2021.
  2. 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
  3. Optimal spatial patterns in feeding, fishing, and pollution, DCDS-S, 2021, preprint
  1. Optimal Stock–Enhancement of a Spatially Distributed Renewable Resource, Journal of Economic Dynamics & Control, 123, 104060, 2021 (mit Th. Upmann, L. Hammann, B. Blasius)

2016–2020

  1. 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)
  1. Stripes on finite domains: Why the zigzag instability is only a partial story, Chaos, 30, 073104, 2020 (mit A. Shapira und A. Yochelis) preprint
  1. 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
  1. Snaking branches of planar BCC fronts in the 3D Brusselator, Physica D, 406, 132383, 2020, (mit D. Wetzel) preprint
  1. 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
  1. Optimal fishery with Coastal Catch, Natural Resource Modelling, e12235, 2019 (mit D. Grass und Th. Upmann) preprint
  1. 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.
  1. 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.

  1. 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)
  1. Desertification by Front Propagation?, Journal of Theoretical Biology 418 (2017), 27–35, (mit Y. Zelnik, U. Feudel und E. Meron) preprint
  1. Optimal management and spatial patterns in a distributed shallow lake model, 1:1-21, 2017, (mit D. Grass), preprint
  1. 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
  1. 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
  1. Optimal control and spatial patterns in a semi arid vegetation system, Natural Resource Modeling, 29:2, 229–258, 2016, preprint
  1. 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

  1. 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
  1. 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
  1. Individual-based model for quorum sensing with background flow, Bull. Math. Biology, (mit J. Müller und B. Hense), 2014, preprint
  1. 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,
  1. 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
  1. Approximating the dynamics of communicating cells in a diffusive medium by ODEs -Â Homogenization with Localization, J. Math. Biology, 2012, (mit J. Müller) preprint
  1. 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
  1. 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
  1. 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
  1. Corrigendum to 38, Proc. Royal Soc. Edinburgh, 141A, 819-824, 2011 (mit R. Kaiser), preprint
  1. 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,
  1. 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
  1. Erratum to (published version of) 42, Physica D, 240, 357-362, 2011 (mit T. Dohnal)preprint
  1. 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

  1. Amplitude equations – an invitation to multiple scale analysis Summer School Modern Computational Science, Oldenburg 2010, Universitätsverlag Oldenburg, 2010, preprint,
  1. Statistics for surface modes of nanoparticles with shape fluctuations, Commun. in Comp. Physics, 8, 1224, 2010, (mit F. Rüting), preprint,
  1. 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
  1. Perturbation theory for plasmonic eigenvalues, Phys. Rev. B, 80:245405, 2009, (mit D. Grieser, S. Biehs, O. Huth, F. Rüting, and M. Holthaus) preprint
  1. An integral boundary layer equation for film flow over inclined wavy bottoms, Phys. of Fluids, 21, 092105, 2009. (mit T. Häcker) preprint
  1. 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
  1. 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)
  1. 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)
  1. A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in 3, Comm. PDE 33:5, 772–783, 2008. (mit A. Melcher and G. Schneider) preprint
  1. A remark about the justification of the nonlinear SchrÃdinger 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
  1. 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
  1. 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
  1. 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
  1. Exponential averaging and traveling waves in rapidly varying periodic media, Mathematische Nachrichten, 280:4, 408-422, 2007 (mit K. Matthies and G. Schneider) preprint
  1. 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
  1. 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
  1. 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
  1. The mathematics of light pulses in dispersive media, Jahresberichte der DMV, 109:3, 139-161, 2007 (mit G. Schneider) preprint
  1. 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
  1. 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
  1. 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

  1. Pattern formation for NO+NH3 on Pt(100) – 2-dimensional numerical results, Phys. Rev.E, 71, 016207, 2005. preprint
  1. 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
  1. 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
  1. Relaxed plasma vacuum states in cylinders. Q.J. Mech. Appl. Math., 57:1, 1–17, 2004. (mit R. Kaiser) preprint
  1. Self–similar decay of localized perturbations in the Integral Boundary Layer equation. Journal Diff. Eq., 207:2, 407–422, 2004.preprint
  1. 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
  1. Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. ZAMP 54, 677-712, 2003. (mit G. Schneider) preprint
  1. Approximation of the Integral Boundary Layer equation by the Kuramoto–Sivashinsky equation. SIAM J. Appl. Math. 63:4, 1359–1377, 2003. preprint
  1. 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
  1. 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
  1. 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
  1. Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Asymptot. Anal. 28:2, 163-180, 2001. (mit G. Schneider) preprint
  1. Stable modulating multi-pulse solutions for dissipative systems with resonant spatially periodic forcing. J. Nonlin. Sci.,11:2, 89-121, 2001. preprint
  1. Diffusive stability of rolls in the two-dimensional real and complex Swift–Hohenberg equation. Comm. PDE 24:11&12, 2109-2146, 1999.preprint

Tagungsbeiträge

  1. 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
  1. Modeling of film flows over inclined wavy bottoms, PAMM 8:10721-10722, 2009 (mit T. Häcker)
  1. Resonance in viscous film flow over topography PAMM 7:4100025–4100026, 2008 (mit C. Heining, A. Wierschem, V. Bontozoglou und N. Aksel)
  1. 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 Equaiff–11: 507–517, 2005. (mit N. Breindl and G. Schneider) preprint
  1. Local in time nonlinear stability of pulses in an unstable medium. XIVth International Congress on Mathematical Physics, Lisboa 2003, 296–303, World Scientific, 2005. (mit R.L. Pego und G. Schneider)
  1. 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)
(Stand: 31.03.2023)  |