Modulation

Chair for Analsys and Modeling

Publications

Publications at the Chair for Analysis and Modeling at the Institute of Analysis, Dynamics and Modeling

Publications 2019

  • Bauer, Roman; Düll, Wolf-Patrick; Schneider, Guido: The KdV, the Burgers, and the Whitham limit for a spatially periodic Boussinesq model, Proceedings A Royal Society Edinburgh 149(1), 2019, 191-217.

Publications 2018

  • W.-P. Düll, B. Hilder, G. Schneider. Analysis of the embedded cell method in 1D for the numerical homogenization of metal-ceramic composite materials. J. Appl. Anal. 24 (2018), no. 1, 71-80.
  • W.-P. Düll. On the mathematical description of time-dependent surface water waves. Jahresber. Dtsch. Math.-Ver. 120 (2018), no. 2, 117-141.
  • W.-P. Düll, M. Heß. Existence of long time solutions and validity of the Nonlinear Schr¨odinger approximation for a quasilinear dispersive equation. J. Differential Equations, 264 (2018), no. 4, 2598-2632.
  • Guillod,Julien; Schneider, Guido; Wittwer, Peter; Zimmermann, Domink: Nonlinear stability at the Eckhaus boundary. SIAM J. Math. Anal. 50-5 (2018), pp. 4699-4720

Previous publications

  • Dmitry Pelinovsky and Guido Schneider. Bifurcations of standing localized waves on periodic graphs. Ann. Henri Poincaré 18: 1185–1211, 2017.
  • Zimmermann, Dominik. A rigorous justification of the Matthews-Cox approximation for the Nikolaevskiy equation, J. Differential Equations 262 (2017), no. 11, 5409–5424.
  • Düll, Wolf-Patrick. Justification of the Nonlinear Schrödinger approximation for a quasilinear Klein-Gordon equation. Comm. Math. Phys. 355(3), 1189-1207, 2017.
  • Markus Daub, Guido Schneider, and Katharina Schratz. From the Klein-Gordon-Zakharov system to the Klein-Gordon equation. Math. Methods Appl. Sci. 39(18) 5371–5380, 2016.
  • Steffen Gilg, Dmitry Pelinovsky, and Guido Schneider. Validity of the NLS approximation for periodic quantum graphs. NoDEA Nonlinear Differential Equations Appl. 23(6), Art. 63, 30 pp., 2016.
  • Wolf-Patrick Düll, Kourosh Sanei Kashani, Guido Schneider. The validity of Whi- tham’s approximation for a Klein-Gordon-Boussinesq model. SIAM J. Math. Anal. 48(6): 4311–4334, 2016.
  • Wolf-Patrick Düll, Kourosh Sanei Kashani, Guido Schneider, and Dominik Zimmermann. Attractivity of the Ginzburg-Landau mode distribution for a pattern forming system with marginally stable long modes. J. Differential Equations 261(1): 319–339, 2016.
  • Wolf-Patrick Düll, Guido Schneider, and C. Eugene Wayne. Justification of the Nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. Arch. Rational Mech. Anal., 220(2), 543–602, 2016.
  • Guido Schneider. Validity and Non-Validity of the Nonlinear Schrödinger equation as a Model for Water Waves. in Lectures on the Theory of Water Waves, ed. by T. Bridges, M.D. Groves and D. Nicholls. Cambridge University Press, London Mathematical Society Lecture Notes Series 426, 121–139, 2016.
  • Wolf-Patrick Düll, Alina Hermann, Guido Schneider, and Dominik Zimmermann. Justification of the 2D NLS equation for a fourth order nonlinear wave equation – quadratic resonances do not matter much in case of analytic initial conditions. J. Math. Anal. Appl. 436(2)2, 847–867, 2016.
  • Guido Schneider, Danish Ali Sunny, and Dominik Zimmermann. The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions. Journal of Dynamics and Differential Equations 27(3), 1077–1099, 2015.
  • Martina Chirilus-Bruckner, Guido Schneider. Interaction of oscillatory packets of water waves. Discrete Contin. Dyn. Syst. 2015, Dynamical systems, differential equations and applications. 10th AIMS Conference. Suppl., 267–275.
  • Martina Chirilus-Bruckner,Wolf-Patrick Düll, and Guido Schneider. NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms. Mathematische Nachrichten 288(2-3) 158–166, 2015.
  • Wolf-Patrick Düll, Andreas Kirchhoff, and Guido Schneider. The existence of bifurcating invariant tori in a spatially extended reaction-diffusion -convection system with spatially localized amplification. J. Nonlinear Sci. 24 (2014), no. 2, 305-358.
  • Christopher Chong, Panayotis G. Kevrekidis, and Guido Schneider. Justification of leading order quasicontinuum approximations of strongly nonlinear lattices. Discrete Contin. Dyn. Syst. 34 (2014), no. 9, 3403–3418.
  • Martina Chirilus-Bruckner, Wolf-Patrick Düll, and Guido Schneider. Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation. J. Math. Anal. Appl. 414 (2014), no. 1, 166-175.
  • Wolf-Patrick Düll. Validity of the Cahn-Hilliard approximation for modulations of slightly unstable pattern in the real Ginzburg-Landau equation. Nonlinear Anal. Real World Appl. 14 (2013), no. 6, 2204-2211.
  • Guido Schneider and Dominik Zimmermann. Justification of the Ginzburg-Landau approximation for an instability as it appears for Marangoni convection. Mathematical Methods in the Applied Sciences 36(9): 1003-1013, 2013.
  • Dmitry Pelinovsky and Guido Schneider. Rigorous justification of the short-pulse equation. Nonlinear Differential Equations and Applications NoDEA 20: 1277-1294, 2013.
  • Christopher Chong and Guido Schneider. Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity. ZAMM 93: 688-696, 2013.
  • Markus Daub. An appropriate bounded invariant region for a bistable reaction-diffusion model of the caspase-3/8 feedback loop, Bull. Math. Biol. 75 (2013), no. 11,  2271-2288.
  • Claus Braun, Markus Daub, Alexander Schöll, Guido Schneider, and Hans-Joachim Wunderlich. Parallel Simulation of Apoptotic Receptor-Clustering on GPGPU Many-Core Architectures, IEEE International Conference on Bioinformatics and Biomedicine (BIBM): 1-6, 2012.
  • Philipp Leube, Wolfgang Nowak, and Guido Schneider: Temporal Moments revisited: Why there is there no better way for physically-based model reduction in time. Water Resources Research 48: doi: 10.1029/2012WR011973. issn: 0043-1397, 2012.
  • Guido Schneider and C. Eugene Wayne. Corrigendum: the long-wave limit for the water wave problem. I: The case of zero surface tension. Commun. Pure Appl. Math. 65(5): 587-591, 2012.
  • Martina Chirilus-Bruckner and Guido Schneider. Detection of standing pulses in periodic media by pulse interaction Journal of Differential Equations 253: 2161-2190, 2012.
  • Vincent Lescarret and Guido Schneider. Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide. ZAMP 63(3): 401-427, 2012.
  • Björn Sandstede, Arnd Scheel, Guido Schneider, and Hannes Uecker. Diffusive mixing of periodic wave trains in reaction-diffusion systems. Journal of Differential equations 252: 3541-3574, 2012 .
  • Tobias Häcker, Guido Schneider, and Hannes Uecker. Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms, Electron. J. Diff. Equ., Vol. 2012(61): 1-51, 2012.
  • Christopher Chong, Dmitry E. Pelinovsky, and Guido Schneider. On the validity of the variational approximation in discrete nonlinear Schrödinger equations. Physica D 241: 115-124, 2012.
  • Martina Chirilus-Bruckner, Christopher Chong, Oskar Prill, and Guido Schneider. Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations. DCDS-S 5(5): 879-901, 2012.
  • Wolf-Patrick Düll. Validity of the Korteweg-de Vries Approximation for the Two-Dimensional Water Wave Problem in the Arc Length Formulation. Comm. Pure Appl. Math. 65, no. 3, 381-429, 2012.
  • Wolf-Patrick Düll. A waiting time phenomenon for modulations of pattern in reaction-diffusion systems. Z. Angew. Math. Phys. 63, no. 1, 1-23, 2012.
  • Markus Daub, Steffen Waldherr, Frank Allgöwer, Peter Scheurich, Guido Schneider. Death wins against life in a spatially extended model of the caspase-3/8 feedback loop, Biosystems 108, 45-51, 2012.
  • Martin Falk, Markus Daub, Guido Schneider, and Thomas Ertl. Modeling and Visualization of Receptor Clustering on the Cellular  Membrane. IE-EE Symposium on Biological Data Visualization (BioVis 2011) (2011), 9-15, DOI:10.1109/BioVis.2011.6094042.
  • Oleg N. Kirillov, Dmitry E. Pelinovsky, and Guido Schneider. Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor flows. Physical Review E 84: 065301(R), 2011.
  • Christopher Chong and Guido Schneider. The validity of the KdV approximation in case of resonances arising from periodic media. J. Math. Anal. Appl. 383(2): 330-336, 2011.
  • Guido Schneider and C. Eugene Wayne. Justification of the NLS approximation for a quasilinear water wave model. Journal of differential equations 251(2): 238-269, 2011.
  • Guido Schneider. The role of the Nonlinear Schrödinger equation in nonlinear optics. In Oberwolfach seminars 42: Photonic Crystals: Mathematical Analysis and Numerical Approximation by W. Dörfler, A. Lechleiter, M. Plum, G. Schneider, and C. Wieners. Birkhäuser 2011.
  • Guido Schneider. Justification of the NLS approximation for the KdV equation using the Miura transformation. Advances in Mathematical Physics, vol. 2011, Article ID 854719, 4 pages, 2011. doi:10.1155/2011/854719.
  • Carsten Blank, Martina Chirilus-Bruckner, Vincent Lescarret, and Guido Schneider. Breather solutions in periodic media. Comm. Math. Phys. 302: 815–841, 2011.
  • Tobias Häcker, Guido Schneider, and Dominik Zimmermann. Justification of the Ginzburg-Landau approximation in case of marginal stable long waves.  Journal of Nonlinear Science 21 (1): 93–113, 2011.
  • Wolf-Patrick Düll, Guido Schneider, and Hannes Uecker. Local existence and uniqueness of solutions of the weak electrolyte model describing electro-convection in nematic liquid crystals. ZAMM 91 (3): 247– 256, 2011.
  • Guido Schneider, Hannes Uecker, and MichaelWand. Interaction of modulated pulses in nonlinear oscillator chains. Journal of Difference Equations and Applications 17 (3): 279–298, 2011.
  • Guido Schneider. Bounds for the Nonlinear Schrödinger approximation of the Fermi-Pasta-Ulam-system. Applicable Analysis 89 (9): 1523–1540, 2010.
  • Dmitry Pelinovsky and Guido Schneider. Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential. J. Differential Equations 248 (4): 837–849, 2010.
  • Wolf-Patrick Düll and Guido Schneider. Validity of Whitham’s equations for the modulation of wave-trains in the NLS equation. J. Nonlinear Science 19(5): 453-466, 2009.
  • Vincent Lescarret, Carsten Blank, Martina Chirilus-Bruckner, Christopher Chong, and Guido Schneider. Standing generalized modulating pulse solutions for a nonlinear wave equation in periodic media. Nonlinearity 22: 1869-1898, 2009.
  • Wolf-Patrick Düll and Guido Schneider. A waiting time phenomenon in pattern forming systems. SIAM Journal on Mathematical Analysis 41(1): 415-433, 2009.
  • Arjen Doelman, Björn Sandstede, Arnd Scheel, and Guido Schneider. The dynamics of modulated wave trains. Memoirs of the American Mathematical Society, Volume 199: 105 pp, 2009.
  • Tomas Dohnal, Dmitry Pelinovsky, and Guido Schneider. Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential. J. Nonlinear Science 19(2): 95-131, 2009.
  • Dmitry Pelinovsky, Guido Schneider, and Robert MacKay. Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential. Comm. Math. Phys. 284: 803-831, 2008.
  • Dmitry Pelinovsky and Guido Schneider. Moving gap solitons in periodic potentials. Math. Meth. Appl. Sci. 31(14):1739-1760, 2008.
  • Andreas Melcher, Guido Schneider, and Hannes Uecker. A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in R3. Communications in Partial Differential Equations, 33(5):772-783, 2008.
  • M. D. Groves and G. Schneider. Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales. Comm. Math. Phys. 278(3): 567-625, 2008.
  • Johannes-Geert Hagmann, Lasha Tkeshelashvili, Guido Schneider, and Kurt Busch. Non-resonant waves in one-dimensional photonic crystals with quadratic nonlinearity. Physical Review A 77: 023809-1-11, 2008.
  • Martina Chirilus Bruckner, Christopher Chong, Guido Schneider, and Hannes Uecker. Separation of internal and interaction dynamics for NLS-described wavepackets with different carrier waves. J. Math. Anal. Appl. 347: 304-314, 2008.
  • Carsten Blank, Martina Chirilus Bruckner, Christopher Chong, Vincent Lescarret, Guido Schneider, and Hannes Uecker. A remark about the justification of the nonlinear Schrödinger equation in quadratic spatially periodic media. ZAMP, Z. Angew. Math. Phys. 59(3): 554-557, 2008.
  • Norbert Breindl, Guido Schneider, and Hannes Uecker. Mathematical theory for the Ginzburg-Landau approximation in semilinear pattern forming systems with time-periodic forcing applied to electro-convection in nematic liquid crystals. Proceedings of the Equadiff 2005: International Conference on Differential Equations. Bratislava 2005. Ed.: M. Fila, A. Handlovicova, K. Mikula, M. Medved, P. Quittner, and D. Sevcovic. Published by Vydavatelastvo STU, Vazovova 5, Bratislava 2007. (ISBN 978-80-227-2624-5)
  • Dmitry Pelinovsky and Guido Schneider. Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Applicable Analysis 86(8): 1017-1036, 2007.
  • Guido Schneider and Hannes Uecker. The mathematics of light pulses in dispersive media. DMV-Jahresbericht 109: 139-161, 2007.
  • Hannes Uecker and Andreas Wirschen. A spatially periodic Kuramoto-Sivashinsky equation as a model problem for inclined film flow over wavy bottom. Electron. J. Differential Equations 2007, No. 118, 18 pp.
  • Wolf-Patrick Düll, The validity of phase diffusion equations and of Cahn-Hilliard equations for the modulation of pattern in reaction-diffusion systems. J. Differential Equations 239 (2007), no. 1, 72–98.
  • Hannes Uecker. Self-similar decay of spatially localized perturbations of the Nusselt solution for the inclined film problem. Arch. Ration. Mech. Anal. 184 (2007), no. 3, 401–447.
  • Martina Chirilus-Bruckner, Guido Schneider, and Hannes Uecker. On the interaction of NLS-described modulating pulses with different carrier waves. Mathematical Methods in Applied Sciences 30: 1965-1978, 2007.
  • Guido Schneider and Hannes Uecker. The amplitude equation for the first instability of electro-convection in nematic liquid crystals in case of two unbounded space directions. Nonlinearity 20: 1361-1386, 2007.
  • Robert L. Pego, Guido Schneider, and Hannes Uecker. Long-time persistence of kdv solitons as transient dynamics in a model of inclined film flow. Proceedings of the Royal Soc. Edinb. 137A:133-146, 2007.
  • Karsten Matthies, Guido Schneider, and Hannes Uecker. Exponential averaging for traveling wave solutions in rapidly varying periodic media. Mathematische Nachrichten, 280:408-422, 2007.
  • Jochen Bitzer and Guido Schneider. Approximation and attractivity properties of the degenerated ginzburg-landau equation. Journal of Mathematical Analysis and Applications 331:743-778, 2007. 
     
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