Edit Profile (opens in new tab) Schneider, Guido Co-Author Distance Author ID: schneider.guido Published as: Schneider, Guido; Schneider, G. Homepage: https://www.iadm.uni-stuttgart.de/team/Schneider-00003/ External Links: MGP · dblp · GND Documents Indexed: 153 Publications since 1992, including 4 Books and 6 Additional arXiv Preprints 4 Contributions as Editor Reviewing Activity: 32 Reviews Co-Authors: 86 Co-Authors with 124 Joint Publications 1,857 Co-Co-Authors all top 5 Co-Authors 32 single-authored 22 Uecker, Hannes 15 Düll, Wolf-Patrick 15 Pelinovsky, Dmitry Efimovich 11 Chirilus-Bruckner, Martina 9 Wayne, Clarence Eugene 9 Zimmermann, Dominik 8 Chong, Christopher 5 de Rijk, Björn 5 Mielke, Alexander 4 Groves, Mark D. 4 Lescarret, Vincent 3 Blank, Carsten 3 Fukuizumi, Reika 3 Haas, Tobias 3 Hilder, Bastian 3 Kunze, Markus 3 Sandstede, Björn 3 Scheel, Arnd 3 Schratz, Katharina 2 Bauer, Roman 2 Baumstark, Simon 2 Blömker, Dirk 2 Doelman, Arjen 2 Dohnal, Tomáš 2 Eckmann, Jean-Pierre 2 Gallay, Thierry 2 Gauß, Nicole 2 Gilg, Steffen 2 Häcker, Tobias 2 Kashani, Kourosh Sanei 2 Maier, Daniela 2 Melbourne, Ian 2 Pego, Robert Leo 2 Sunny, Danish Ali 2 Wörner, Maximilian 1 Bianchi, Luigi Amedeo 1 Bitzer, Jochen 1 Bollerman, Peter 1 Brand, Thomas 1 Breindl, Norbert 1 Bridges, Thomas J. 1 Busch, Kurt 1 Craig, Walter 1 Cummings, Patrick 1 Daub, Markus 1 de Derijk, Björn 1 Dorfler, Willy 1 Gao, Yueyuan 1 Giannoulis, Ioannis 1 Griesemer, Marcel 1 Guillod, Julien 1 Hărăguş-Courcelle, Mariana 1 Hermann, Alina 1 Heß, Max 1 James, Guillaume 1 Kevrekidis, Panayotis G. 1 Kirchhoff, Andreas 1 Kirillov, Oleg N. 1 Kirrmann, Pius 1 Kostianko, Anna 1 Lamm, Tobias 1 Lechleiter, Armin 1 Liero, Matthias 1 Logioti, Anna 1 MacKay, Robert Sinclair 1 Maier-Paape, Stanislaus 1 Marzuola, Jeremy Louis 1 Matthies, Karsten 1 Melcher, Andreas 1 Müller, Johannes 1 Peterhof, Daniela 1 Plum, Michael 1 Prill, Oskar 1 Rapti, Zoi 1 Reichel, Wolfgang 1 Reichelt, Sina 1 Schmid, Jochen 1 Seelbach, Thorsten 1 Stuart, Charles Alexander 1 Takahashi, Motomitsu 1 Taraca, Raphael 1 Theil, Florian 1 Thomas, Marita 1 Tkeshelashvili, Lasha 1 van Harten, Aart 1 Wand, Michael 1 Wieners, Christian 1 Winter, Matthias 1 Wittwer, Peter 1 Ziegra, Andreas 1 Zink, Oliver all top 5 Serials 11 Journal of Differential Equations 9 Communications in Mathematical Physics 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Mathematische Nachrichten 7 Journal of Nonlinear Science 7 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Journal of Mathematical Analysis and Applications 6 Mathematical Methods in the Applied Sciences 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 NoDEA. Nonlinear Differential Equations and Applications 4 Archive for Rational Mechanics and Analysis 4 Physica D 4 SIAM Journal on Mathematical Analysis 3 Applicable Analysis 3 Nonlinearity 3 Oberwolfach Reports 3 Discrete and Continuous Dynamical Systems. Series S 2 Communications on Pure and Applied Mathematics 2 Letters in Mathematical Physics 2 Indiana University Mathematics Journal 2 European Journal of Applied Mathematics 2 SIAM Journal on Applied Mathematics 2 Journal of Dynamics and Differential Equations 2 Discrete and Continuous Dynamical Systems 2 Journal of Applied Analysis 2 Discrete and Continuous Dynamical Systems. Series B 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Wave Motion 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Memoirs of the American Mathematical Society 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Applied Mathematics Letters 1 Asymptotic Analysis 1 Differential and Integral Equations 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Electronic Journal of Differential Equations (EJDE) 1 Journal of Difference Equations and Applications 1 Communications in Applied Analysis 1 Chaos 1 Interdisciplinary Information Sciences (IIS) 1 Annales Henri Poincaré 1 Nonlinear Analysis. Real World Applications 1 SIAM Journal on Applied Dynamical Systems 1 Graduate Studies in Mathematics 1 Oberwolfach Seminars 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Advances in Mathematical Physics 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 141 Partial differential equations (35-XX) 48 Fluid mechanics (76-XX) 28 Dynamical systems and ergodic theory (37-XX) 12 Optics, electromagnetic theory (78-XX) 8 Ordinary differential equations (34-XX) 5 Quantum theory (81-XX) 4 General and overarching topics; collections (00-XX) 3 Mechanics of deformable solids (74-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Biology and other natural sciences (92-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 115 Publications have been cited 1,694 times in 736 Documents Cited by ▼ Year ▼ The validity of modulation equations for extended systems with cubic nonlinearities. Zbl 0786.35122 Kirrmann, Pius; Schneider, Guido; Mielke, Alexander 90 1992 The long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1034.76011 Schneider, Guido; Wayne, C. Eugene 89 2000 Attractors for modulation equations on unbounded domains – existence and comparison. Zbl 0833.35016 Mielke, Alexander; Schneider, Guido 86 1995 The dynamics of modulated wave trains. Zbl 1179.35005 Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 72 2009 Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation. Zbl 0861.35107 Schneider, Guido 51 1996 Validity and limitation of the Newell-Whitehead equation. Zbl 0844.35120 Schneider, Guido 46 1995 The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006 Schneider, Guido; Wayne, C. Eugene 45 2002 Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model. Zbl 0970.35126 Schneider, Guido; Wayne, C. Eugene 44 2000 Error estimates for the Ginzburg-Landau approximation. Zbl 0805.35125 Schneider, Guido 39 1994 Propagation of hexagonal patterns near onset. Zbl 1044.37049 Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 38 2003 Nonlinear PDEs. A dynamical systems approach. Zbl 1402.35001 Schneider, Guido; Uecker, Hannes 38 2017 Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances. Zbl 1075.35080 Schneider, Guido 34 2005 Bifurcations of standing localized waves on periodic graphs. Zbl 1387.35556 Pelinovsky, Dmitry; Schneider, Guido 33 2017 Photonic crystals. Mathematical analysis and numerical approximation. Zbl 1238.78001 Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian 32 2011 Justification of modulation equations for hyperbolic systems via normal forms. Zbl 0890.35082 Schneider, Guido 30 1998 Diffusive mixing of periodic wave trains in reaction-diffusion systems. Zbl 1298.35108 Sandstede, Björn; Scheel, Arnd; Schneider, Guido; Uecker, Hannes 29 2012 Nonlinear diffusive stability of spatially periodic solutions – abstract theorem and higher space dimensions –. Zbl 0907.35015 Schneider, Guido 27 1998 Kawahara dynamics in dispersive media. Zbl 0977.35123 Schneider, Guido; Wayne, C. Eugene 27 2001 Justification of the nonlinear Schrödinger equation in spatially periodic media. Zbl 1109.35104 Busch, Kurt; Schneider, Guido; Tkeshelashvili, Lasha; Uecker, Hannes 27 2006 The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions. Zbl 1344.35138 Schneider, Guido; Sunny, Danish Ali; Zimmermann, Dominik 25 2015 KP description of unidirectional long waves. The model case. Zbl 1015.76015 Gallay, Thierry; Schneider, Guido 24 2001 Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178 Schneider, Guido; Wayne, C. Eugene 23 2011 Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. Zbl 1334.35313 Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene 23 2016 A new estimate for the Ginzburg-Landau approximation on the real axis. Zbl 0803.35139 Schneider, G. 22 1994 Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations. Zbl 1248.35182 Chirilus-Bruckner, Martina; Chong, Christopher; Prill, Oskar; Schneider, Guido 21 2012 Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential. Zbl 1186.35207 Pelinovsky, Dmitry; Schneider, Guido 21 2010 Nonlinear stability of Taylor vortices in infinite cylinders. Zbl 0916.76022 Schneider, Guido 20 1998 Global existence results for pattern forming processes in infinite cylindrical domains – applications to 3D Navier-Stokes problems. Zbl 0933.35025 Schneider, Guido 17 1999 Justification of the nonlinear Schrödinger equation for a resonant Boussinesq model. Zbl 1194.35362 Düll, Wolf-Patrick; Schneider, Guido 17 2006 Bifurcating fronts for the Taylor-Couette problem in infinite cylinders. Zbl 0922.35015 Hărağuş-Courcelle, Mariana; Schneider, Guido 17 1999 Validity of the NLS approximation for periodic quantum graphs. Zbl 1367.35156 Gilg, Steffen; Pelinovsky, Dmitry; Schneider, Guido 17 2016 Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential. Zbl 1162.47059 Pelinovsky, Dmitry; Schneider, Guido; MacKay, Robert S. 16 2008 Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Zbl 1132.41344 Pelinovsky, Dmitry; Schneider, Guido 15 2007 Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Zbl 0988.35158 Schneider, Guido; Uecker, Hannes 15 2001 Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential. Zbl 1177.35216 Dohnal, Tomáš; Pelinovsky, Dmitry; Schneider, Guido 15 2009 Long-time persistence of Korteweg-de Vries solitons as transient dynamics in a model of inclined film flow. Zbl 1174.35102 Pego, Robert L.; Schneider, Guido; Uecker, Hannes 14 2007 The validity of generalized Ginzburg-Landau equations. Zbl 0874.35050 Schneider, Guido 14 1996 The stochastic Landau equation as an amplitude equation. Zbl 1004.60074 Blömker, D.; Maier-Paape, S.; Schneider, G. 14 2001 Justification of the Ginzburg-Landau approximation in case of marginally stable long waves. Zbl 1209.35010 Häcker, Tobias; Schneider, Guido; Zimmermann, Dominik 13 2011 Breather solutions in periodic media. Zbl 1223.35234 Blank, Carsten; Chirilus-Bruckner, Martina; Lescarret, Vincent; Schneider, Guido 13 2011 Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation. Zbl 0940.35179 Schneider, Guido 13 1998 Non-linear stability of modulated fronts for the Swift-Hohenberg equation. Zbl 0994.35057 Eckmann, J.-P.; Schneider, G. 13 2002 Rigorous justification of the short-pulse equation. Zbl 1268.35089 Pelinovsky, Dmitry; Schneider, Guido 13 2013 Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. Zbl 1041.35074 Schneider, Guido; Uecker, Hannes 12 2003 Comparison of inertial manifolds and application to modulated systems. Zbl 0957.35025 Mielke, A.; Schneider, G.; Ziegra, A. 12 2000 The long wave limit for a Boussinesq equation. Zbl 0911.35105 Schneider, Guido 12 1998 Validity of Whitham’s equations for the modulation of periodic traveling waves in the NLS equation. Zbl 1179.35305 Düll, Wolf-Patrick; Schneider, Guido 12 2009 Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations. Zbl 0803.35140 Schneider, Guido 12 1994 Stable transport of information near essentially unstable localized structures. Zbl 1055.35021 Gallay, Thierry; Schneider, Guido; Uecker, Hannes 11 2004 Modulating pulse solutions for quasilinear wave equations. Zbl 1078.35074 Groves, Mark D.; Schneider, Guido 11 2005 Hopf bifurcation in spatially extended reaction-diffusion systems. Zbl 0899.58048 Schneider, G. 11 1998 Justification of the Ginzburg-Landau approximation for an instability as it appears for Marangoni convection. Zbl 1285.35114 Schneider, Guido; Zimmermann, Dominik 11 2013 Analyticity of Ginzburg-Landau modes. Zbl 0832.35021 Schneider, Guido 10 1995 Modulating pulse solutions for a class of nonlinear wave equations. Zbl 0981.35041 Groves, M. D.; Schneider, G. 10 2001 Phase dynamics in the real Ginzburg-Landau equation. Zbl 1057.35064 Melbourne, Ian; Schneider, Guido 10 2004 Hopf bifurcation and exchange of stability in diffusive media. Zbl 1064.35021 Brand, Thomas; Kunze, Markus; Schneider, Guido; Seelbach, Thorsten 10 2004 Bounds for the nonlinear Schrödinger approximation of the Fermi-Pasta-Ulam system. Zbl 1194.35427 Schneider, Guido 10 2010 On the justification of the Ginzburg-Landau approximation. Zbl 0836.35147 Bollerman, P.; van Harten, A.; Schneider, G. 9 1995 Phase dynamics in the complex Ginzburg-Landau equation. Zbl 1059.35139 Melbourne, Ian; Schneider, Guido 9 2004 Justification of the NLS approximation for the KdV equation using the Miura transformation. Zbl 1417.37251 Schneider, Guido 9 2011 A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in \(\mathbb R^{3}\). Zbl 1153.37389 Melcher, Andreas; Schneider, Guido; Uecker, Hannes 9 2008 Modulation equation and SPDEs on unbounded domains. Zbl 1435.35292 Bianchi, Luigi Amedeo; Blömker, Dirk; Schneider, Guido 9 2019 The amplitude equations for the first instability of electro-convection in nematic liquid crystals in the case of two unbounded space directions. Zbl 1116.76030 Schneider, Guido; Uecker, Hannes 8 2007 Derivation and justification of the complex Ginzburg-Landau equation as a modulation equation. Zbl 0856.35060 Mielke, Alexander; Schneider, Guido 8 1996 On the validity of the variational approximation in discrete nonlinear Schrödinger equations. Zbl 1252.35247 Chong, Christopher; Pelinovsky, Dmitry E.; Schneider, Guido 8 2012 Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401 Schneider, Guido; Wayne, C. Eugene 8 2003 From the Klein-Gordon-Zakharov system to the Klein-Gordon equation. Zbl 1352.35072 Daub, Markus; Schneider, Guido; Schratz, Katharina 8 2016 Stability and diffusive dynamics on extended domains. Zbl 1004.35018 Mielke, Alexander; Schneider, Guido; Uecker, Hannes 8 2001 Nonlinear stability of bifurcating front solutions for the Taylor-Couette problem. Zbl 0967.35109 Eckmann, J.-P.; Schneider, G. 7 2000 On the validity of 2D surface water wave models. Zbl 1096.76504 Schneider, Guido; Wayne, C. Eugene 7 2002 Cahn-Hilliard description of secondary flows of a viscous incompressible fluid in an unbounded domain. Zbl 0929.76043 Schneider, G. 6 1999 Justification of mean-field coupled modulation equations. Zbl 0880.35108 Schneider, Guido 6 1997 On the interaction of NLS-described modulating pulses with different carrier waves. Zbl 1149.35392 Chirilus-Bruckner, Martina; Schneider, Guido; Uecker, Hannes 6 2007 NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms. Zbl 1311.35164 Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido 6 2015 Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves. Zbl 1159.35066 Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido; Uecker, Hannes 6 2008 Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales. Zbl 1160.35052 Groves, M. D.; Schneider, G. 5 2008 Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation. Zbl 1315.35185 Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido 5 2014 Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves. Zbl 1360.76061 Schneider, Guido 5 2016 Effective slow dynamics models for a class of dispersive systems. Zbl 1452.35014 Baumstark, Simon; Schneider, Guido; Schratz, Katharina; Zimmermann, Dominik 5 2020 Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity. Zbl 1280.35133 Chong, Christopher; Schneider, Guido 5 2013 The monoatomic FPU system as a limit of a diatomic FPU system. Zbl 1442.35456 Pelinovsky, Dmitry E.; Schneider, Guido 5 2020 Corrigendum: the long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1236.76016 Schneider, Guido; Wayne, C. Eugene 4 2012 Some characterizations of the Taylor-Couette attractor. Zbl 1012.35011 Schneider, Guido 4 1999 Justification of the equations for the resonant four wave interaction. Zbl 1100.76013 Schneider, Guido; Zink, Oliver 4 2005 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. Zbl 1333.35251 Düll, Wolf-Patrick; Hermann, Alina; Schneider, Guido; Zimmermann, Dominik 4 2016 Almost global existence and transient self similar decay for Poiseuille flow at criticality for exponentially long times. Zbl 1058.76065 Schneider, Guido; Uecker, Hannes 4 2003 A proof of validity for multiphase Whitham modulation theory. Zbl 1472.35332 Bridges, Thomas J.; Kostianko, Anna; Schneider, Guido 4 2020 Exponential averaging for traveling wave solutions in rapidly varying periodic media. Zbl 1206.35146 Matthies, Karsten; Schneider, Guido; Uecker, Hannes 3 2007 Detection of standing pulses in periodic media by pulse interaction. Zbl 1259.78030 Chirilus-Bruckner, Martina; Schneider, Guido 3 2012 A waiting time phenomenon in pattern forming systems. Zbl 1190.35029 Düll, Wolf-Patrick; Schneider, Guido 3 2009 Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum. Zbl 1063.35029 Kunze, M.; Schneider, G. 3 2004 The mathematics of light pulses in dispersive media. Zbl 1204.35002 Schneider, Guido; Uecker, Hannes 3 2007 Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide. Zbl 1253.35173 Lescarret, Vincent; Schneider, Guido 3 2012 On the dynamics of the mean-field polaron in the high-frequency limit. Zbl 1436.35289 Griesemer, Marcel; Schmid, Jochen; Schneider, Guido 3 2017 Nonlinear stability at the Eckhaus boundary. Zbl 1454.35361 Guillod, Julien; Schneider, Guido; Wittwer, Peter; Zimmermann, Dominik 3 2018 Failure of the \(N\)-wave interaction approximation without imposing periodic boundary conditions. Zbl 07806611 Haas, Tobias; Schneider, Guido 3 2020 Aproximation and attractivity properties of the degenerated Ginzburg-Landau equation. Zbl 1117.35033 Bitzer, Jochen; Schneider, Guido 2 2007 The validity of the KdV approximation in case of resonances arising from periodic media. Zbl 1241.35175 Chong, Christopher; Schneider, Guido 2 2011 Interaction of modulated pulses in nonlinear oscillator chains. Zbl 1228.34026 Schneider, Guido; Uecker, Hannes; Wand, Michael 2 2011 Existence and stability of modulating pulse-solutions in a phenomenological model of nonlinear optics. Zbl 0954.35148 Schneider, Guido 2 2000 KP-II approximation for a scalar Fermi-Pasta-Ulam system on a 2D square lattice. Zbl 1517.37077 Pelinovsky, Dmitry; Schneider, Guido 2 2023 Effective slow dynamics models for a class of dispersive systems. Zbl 1452.35014 Baumstark, Simon; Schneider, Guido; Schratz, Katharina; Zimmermann, Dominik 5 2020 The monoatomic FPU system as a limit of a diatomic FPU system. Zbl 1442.35456 Pelinovsky, Dmitry E.; Schneider, Guido 5 2020 A proof of validity for multiphase Whitham modulation theory. Zbl 1472.35332 Bridges, Thomas J.; Kostianko, Anna; Schneider, Guido 4 2020 Failure of the \(N\)-wave interaction approximation without imposing periodic boundary conditions. Zbl 07806611 Haas, Tobias; Schneider, Guido 3 2020 Global existence and decay in nonlinearly coupled reaction-diffusion-advection equations with different velocities. Zbl 1435.35198 de Rijk, Björn; Schneider, Guido 1 2020 Modulation equation and SPDEs on unbounded domains. Zbl 1435.35292 Bianchi, Luigi Amedeo; Blömker, Dirk; Schneider, Guido 9 2019 A model for the periodic water wave problem and its long wave amplitude equations. Zbl 1442.35322 Bauer, Roman; Cummings, Patrick; Schneider, Guido 1 2019 The Korteweg-de Vries, Burgers and Whitham limits for a spatially periodic Boussinesq model. Zbl 1421.35319 Bauer, Roman; Düll, Wolf-Patrick; Schneider, Guido 1 2019 Nonlinear stability at the Eckhaus boundary. Zbl 1454.35361 Guillod, Julien; Schneider, Guido; Wittwer, Peter; Zimmermann, Dominik 3 2018 Nonlinear PDEs. A dynamical systems approach. Zbl 1402.35001 Schneider, Guido; Uecker, Hannes 38 2017 Bifurcations of standing localized waves on periodic graphs. Zbl 1387.35556 Pelinovsky, Dmitry; Schneider, Guido 33 2017 On the dynamics of the mean-field polaron in the high-frequency limit. Zbl 1436.35289 Griesemer, Marcel; Schmid, Jochen; Schneider, Guido 3 2017 Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. Zbl 1334.35313 Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene 23 2016 Validity of the NLS approximation for periodic quantum graphs. Zbl 1367.35156 Gilg, Steffen; Pelinovsky, Dmitry; Schneider, Guido 17 2016 From the Klein-Gordon-Zakharov system to the Klein-Gordon equation. Zbl 1352.35072 Daub, Markus; Schneider, Guido; Schratz, Katharina 8 2016 Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves. Zbl 1360.76061 Schneider, Guido 5 2016 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. Zbl 1333.35251 Düll, Wolf-Patrick; Hermann, Alina; Schneider, Guido; Zimmermann, Dominik 4 2016 Attractivity of the Ginzburg-Landau mode distribution for a pattern forming system with marginally stable long modes. Zbl 1341.35152 Düll, Wolf-Patrick; Kashani, Kourosh Sanei; Schneider, Guido; Zimmermann, Dominik 2 2016 The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions. Zbl 1344.35138 Schneider, Guido; Sunny, Danish Ali; Zimmermann, Dominik 25 2015 NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms. Zbl 1311.35164 Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido 6 2015 Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation. Zbl 1315.35185 Chirilus-Bruckner, Martina; Düll, Wolf-Patrick; Schneider, Guido 5 2014 Justification of leading order quasicontinuum approximations of strongly nonlinear lattices. Zbl 1307.35256 Chong, Christopher; Kevrekidis, P. G.; Schneider, Guido 2 2014 Rigorous justification of the short-pulse equation. Zbl 1268.35089 Pelinovsky, Dmitry; Schneider, Guido 13 2013 Justification of the Ginzburg-Landau approximation for an instability as it appears for Marangoni convection. Zbl 1285.35114 Schneider, Guido; Zimmermann, Dominik 11 2013 Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity. Zbl 1280.35133 Chong, Christopher; Schneider, Guido 5 2013 Diffusive mixing of periodic wave trains in reaction-diffusion systems. Zbl 1298.35108 Sandstede, Björn; Scheel, Arnd; Schneider, Guido; Uecker, Hannes 29 2012 Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations. Zbl 1248.35182 Chirilus-Bruckner, Martina; Chong, Christopher; Prill, Oskar; Schneider, Guido 21 2012 On the validity of the variational approximation in discrete nonlinear Schrödinger equations. Zbl 1252.35247 Chong, Christopher; Pelinovsky, Dmitry E.; Schneider, Guido 8 2012 Corrigendum: the long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1236.76016 Schneider, Guido; Wayne, C. Eugene 4 2012 Detection of standing pulses in periodic media by pulse interaction. Zbl 1259.78030 Chirilus-Bruckner, Martina; Schneider, Guido 3 2012 Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide. Zbl 1253.35173 Lescarret, Vincent; Schneider, Guido 3 2012 Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms. Zbl 1236.35122 Häcker, Tobias; Schneider, Guido; Uecker, Hannes 2 2012 Photonic crystals. Mathematical analysis and numerical approximation. Zbl 1238.78001 Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian 32 2011 Justification of the NLS approximation for a quasilinear water wave model. Zbl 1225.35178 Schneider, Guido; Wayne, C. Eugene 23 2011 Justification of the Ginzburg-Landau approximation in case of marginally stable long waves. Zbl 1209.35010 Häcker, Tobias; Schneider, Guido; Zimmermann, Dominik 13 2011 Breather solutions in periodic media. Zbl 1223.35234 Blank, Carsten; Chirilus-Bruckner, Martina; Lescarret, Vincent; Schneider, Guido 13 2011 Justification of the NLS approximation for the KdV equation using the Miura transformation. Zbl 1417.37251 Schneider, Guido 9 2011 The validity of the KdV approximation in case of resonances arising from periodic media. Zbl 1241.35175 Chong, Christopher; Schneider, Guido 2 2011 Interaction of modulated pulses in nonlinear oscillator chains. Zbl 1228.34026 Schneider, Guido; Uecker, Hannes; Wand, Michael 2 2011 Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential. Zbl 1186.35207 Pelinovsky, Dmitry; Schneider, Guido 21 2010 Bounds for the nonlinear Schrödinger approximation of the Fermi-Pasta-Ulam system. Zbl 1194.35427 Schneider, Guido 10 2010 The dynamics of modulated wave trains. Zbl 1179.35005 Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 72 2009 Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential. Zbl 1177.35216 Dohnal, Tomáš; Pelinovsky, Dmitry; Schneider, Guido 15 2009 Validity of Whitham’s equations for the modulation of periodic traveling waves in the NLS equation. Zbl 1179.35305 Düll, Wolf-Patrick; Schneider, Guido 12 2009 A waiting time phenomenon in pattern forming systems. Zbl 1190.35029 Düll, Wolf-Patrick; Schneider, Guido 3 2009 Standing generalized modulating pulse solutions for a nonlinear wave equation in periodic media. Zbl 1262.35169 Lescarret, Vincent; Blank, Carsten; Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido 2 2009 Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential. Zbl 1162.47059 Pelinovsky, Dmitry; Schneider, Guido; MacKay, Robert S. 16 2008 A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in \(\mathbb R^{3}\). Zbl 1153.37389 Melcher, Andreas; Schneider, Guido; Uecker, Hannes 9 2008 Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves. Zbl 1159.35066 Chirilus-Bruckner, Martina; Chong, Christopher; Schneider, Guido; Uecker, Hannes 6 2008 Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales. Zbl 1160.35052 Groves, M. D.; Schneider, G. 5 2008 Moving gap solitons in periodic potentials. Zbl 1156.35465 Pelinovsky, Dmitry; Schneider, Guido 2 2008 Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Zbl 1132.41344 Pelinovsky, Dmitry; Schneider, Guido 15 2007 Long-time persistence of Korteweg-de Vries solitons as transient dynamics in a model of inclined film flow. Zbl 1174.35102 Pego, Robert L.; Schneider, Guido; Uecker, Hannes 14 2007 The amplitude equations for the first instability of electro-convection in nematic liquid crystals in the case of two unbounded space directions. Zbl 1116.76030 Schneider, Guido; Uecker, Hannes 8 2007 On the interaction of NLS-described modulating pulses with different carrier waves. Zbl 1149.35392 Chirilus-Bruckner, Martina; Schneider, Guido; Uecker, Hannes 6 2007 Exponential averaging for traveling wave solutions in rapidly varying periodic media. Zbl 1206.35146 Matthies, Karsten; Schneider, Guido; Uecker, Hannes 3 2007 The mathematics of light pulses in dispersive media. Zbl 1204.35002 Schneider, Guido; Uecker, Hannes 3 2007 Aproximation and attractivity properties of the degenerated Ginzburg-Landau equation. Zbl 1117.35033 Bitzer, Jochen; Schneider, Guido 2 2007 Justification of the nonlinear Schrödinger equation in spatially periodic media. Zbl 1109.35104 Busch, Kurt; Schneider, Guido; Tkeshelashvili, Lasha; Uecker, Hannes 27 2006 Justification of the nonlinear Schrödinger equation for a resonant Boussinesq model. Zbl 1194.35362 Düll, Wolf-Patrick; Schneider, Guido 17 2006 Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances. Zbl 1075.35080 Schneider, Guido 34 2005 Modulating pulse solutions for quasilinear wave equations. Zbl 1078.35074 Groves, Mark D.; Schneider, Guido 11 2005 Justification of the equations for the resonant four wave interaction. Zbl 1100.76013 Schneider, Guido; Zink, Oliver 4 2005 Local in time and space nonlinear stability of pulses in an unstable medium. Zbl 1106.76032 Schneider, Guido; Pego, Robert L.; Uecker, Hannes 1 2005 Estimates for the KdV-limit of the Camassa-Holm equation. Zbl 1084.35074 Kunze, Markus; Schneider, Guido 1 2005 Stable transport of information near essentially unstable localized structures. Zbl 1055.35021 Gallay, Thierry; Schneider, Guido; Uecker, Hannes 11 2004 Phase dynamics in the real Ginzburg-Landau equation. Zbl 1057.35064 Melbourne, Ian; Schneider, Guido 10 2004 Hopf bifurcation and exchange of stability in diffusive media. Zbl 1064.35021 Brand, Thomas; Kunze, Markus; Schneider, Guido; Seelbach, Thorsten 10 2004 Phase dynamics in the complex Ginzburg-Landau equation. Zbl 1059.35139 Melbourne, Ian; Schneider, Guido 9 2004 Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum. Zbl 1063.35029 Kunze, M.; Schneider, G. 3 2004 Validity of the Ginzburg-Landau approximation in pattern forming systems with time periodic forcing. Zbl 1093.35035 Breindl, Norbert; Schneider, Guido; Uecker, Hannes 1 2004 Propagation of hexagonal patterns near onset. Zbl 1044.37049 Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 38 2003 Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. Zbl 1041.35074 Schneider, Guido; Uecker, Hannes 12 2003 Estimates for the three-wave interaction of surface water waves. Zbl 1143.76401 Schneider, Guido; Wayne, C. Eugene 8 2003 Almost global existence and transient self similar decay for Poiseuille flow at criticality for exponentially long times. Zbl 1058.76065 Schneider, Guido; Uecker, Hannes 4 2003 The rigorous approximation of long-wavelength capillary-gravity waves. Zbl 1055.76006 Schneider, Guido; Wayne, C. Eugene 45 2002 Non-linear stability of modulated fronts for the Swift-Hohenberg equation. Zbl 0994.35057 Eckmann, J.-P.; Schneider, G. 13 2002 On the validity of 2D surface water wave models. Zbl 1096.76504 Schneider, Guido; Wayne, C. Eugene 7 2002 Kawahara dynamics in dispersive media. Zbl 0977.35123 Schneider, Guido; Wayne, C. Eugene 27 2001 KP description of unidirectional long waves. The model case. Zbl 1015.76015 Gallay, Thierry; Schneider, Guido 24 2001 Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Zbl 0988.35158 Schneider, Guido; Uecker, Hannes 15 2001 The stochastic Landau equation as an amplitude equation. Zbl 1004.60074 Blömker, D.; Maier-Paape, S.; Schneider, G. 14 2001 Modulating pulse solutions for a class of nonlinear wave equations. Zbl 0981.35041 Groves, M. D.; Schneider, G. 10 2001 Stability and diffusive dynamics on extended domains. Zbl 1004.35018 Mielke, Alexander; Schneider, Guido; Uecker, Hannes 8 2001 Bifurcation analysis for a spatially extended random walk system in mathematical biology. Zbl 1084.35545 Schneider, Guido; Müller, Johannes 1 2001 The long-wave limit for the water wave problem. I: The case of zero surface tension. Zbl 1034.76011 Schneider, Guido; Wayne, C. Eugene 89 2000 Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model. Zbl 0970.35126 Schneider, Guido; Wayne, C. Eugene 44 2000 Comparison of inertial manifolds and application to modulated systems. Zbl 0957.35025 Mielke, A.; Schneider, G.; Ziegra, A. 12 2000 Nonlinear stability of bifurcating front solutions for the Taylor-Couette problem. Zbl 0967.35109 Eckmann, J.-P.; Schneider, G. 7 2000 Existence and stability of modulating pulse-solutions in a phenomenological model of nonlinear optics. Zbl 0954.35148 Schneider, Guido 2 2000 Global existence results for pattern forming processes in infinite cylindrical domains – applications to 3D Navier-Stokes problems. Zbl 0933.35025 Schneider, Guido 17 1999 Bifurcating fronts for the Taylor-Couette problem in infinite cylinders. Zbl 0922.35015 Hărağuş-Courcelle, Mariana; Schneider, Guido 17 1999 Cahn-Hilliard description of secondary flows of a viscous incompressible fluid in an unbounded domain. Zbl 0929.76043 Schneider, G. 6 1999 Some characterizations of the Taylor-Couette attractor. Zbl 1012.35011 Schneider, Guido 4 1999 Justification of modulation equations for hyperbolic systems via normal forms. Zbl 0890.35082 Schneider, Guido 30 1998 Nonlinear diffusive stability of spatially periodic solutions – abstract theorem and higher space dimensions –. Zbl 0907.35015 Schneider, Guido 27 1998 Nonlinear stability of Taylor vortices in infinite cylinders. Zbl 0916.76022 Schneider, Guido 20 1998 Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation. Zbl 0940.35179 Schneider, Guido 13 1998 The long wave limit for a Boussinesq equation. Zbl 0911.35105 Schneider, Guido 12 1998 ...and 15 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 808 Authors 83 Schneider, Guido 28 Scheel, Arnd 25 Pelinovsky, Dmitry Efimovich 21 Zumbrun, Kevin R. 18 Düll, Wolf-Patrick 17 Johnson, Mathew A. 17 Uecker, Hannes 16 Blömker, Dirk 14 Mielke, Alexander 13 Dohnal, Tomáš 13 Sandstede, Björn 12 de Rijk, Björn 11 Rodrigues, Luis Miguel 10 Bambusi, Dario 10 Dovetta, Simone 9 Bridges, Thomas J. 9 Chirilus-Bruckner, Martina 9 Noble, Pascal 9 Wayne, Clarence Eugene 8 Kühn, Christian 8 Pu, Xueke 8 Zelik, Sergey V. 8 Zimmermann, Dominik 7 Coclite, Giuseppe Maria 7 Di Ruvo, Lorenzo 7 Gao, Hongjun 7 Jung, Soyeun 7 Kalisch, Henrik 7 Lannes, David 6 Barker, Blake 6 Beck, Margaret 6 Craig, Walter 6 Doelman, Arjen 6 Duan, Jinqiao 6 Haragus, Mariana 6 Israwi, Samer 6 Jaramillo, Gabriela 6 Latushkin, Yuri 6 Rademacher, Jens Diederich Michael 6 Ratliff, Daniel J. 6 Sulem, Catherine 6 Wright, J. Douglas 5 Cholewa, Jan W. 5 Chong, Christopher 5 Dlotko, Tomasz W. 5 Gallay, Thierry 5 Goh, Ryan N. 5 Guo, Boling 5 Guo, Yanfeng 5 Herrmann, Michael 5 Hilder, Bastian 5 Liu, Huimin 5 Matthies, Karsten 5 Mederski, Jarosław 5 Mohammed, Wael W. 5 Sacchetti, Andrea 5 Schratz, Katharina 4 Adami, Riccardo 4 Avery, Montie 4 Bianchi, Luigi Amedeo 4 Bona, Jerry Lloyd 4 Erkip, Albert Kohen 4 Faver, Timothy E. 4 Ghazaryan, Anna 4 Giannoulis, Johannes 4 Guyenne, Philippe 4 Hupkes, Hermen Jan 4 James, Guillaume 4 Jones, Christopher K. R. T. 4 Kairzhan, Adilbek 4 Kevrekidis, Panayotis G. 4 Khrabustovskyi, Andrii 4 Lloyd, David J. B. 4 Noja, Diego 4 Paleari, Simone 4 Perkins, Wesley R. 4 Reichel, Wolfgang 4 Serra, Enrico 4 Sparber, Christof 4 Sun, Chunyou 4 Susanto, Hadi 4 Tentarelli, Lorenzo 4 Tilli, Paolo 4 Wang, Ying 3 Ablowitz, Mark Jay 3 Alazard, Thomas 3 Babin, Anatoli V. 3 Bu, Charles 3 Choi, Yuncherl 3 Colin, Thierry 3 Dangelmayr, Gerhard 3 Duchêne, Vincent 3 Erbay, Saadet 3 Figotin, Alexander 3 Fukuizumi, Reika 3 Groves, Mark D. 3 Guo, Chunxiao 3 Ha, Taeyoung 3 Haas, Tobias 3 Hairer, Martin ...and 708 more Authors all top 5 Cited in 175 Serials 55 Journal of Differential Equations 51 Physica D 29 Nonlinearity 28 Archive for Rational Mechanics and Analysis 25 Journal of Nonlinear Science 23 Journal of Mathematical Analysis and Applications 22 Communications in Mathematical Physics 19 Journal of Dynamics and Differential Equations 18 SIAM Journal on Applied Dynamical Systems 17 SIAM Journal on Mathematical Analysis 16 Discrete and Continuous Dynamical Systems 15 Mathematical Methods in the Applied Sciences 14 ZAMP. 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Analysis and Computations 2 Journal of Elliptic and Parabolic Equations 2 Annales Henri Lebesgue 1 International Journal of Control 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Fluid Mechanics 1 Journal of Mathematical Biology 1 Physica A ...and 75 more Serials all top 5 Cited in 31 Fields 626 Partial differential equations (35-XX) 156 Fluid mechanics (76-XX) 155 Dynamical systems and ergodic theory (37-XX) 59 Ordinary differential equations (34-XX) 55 Numerical analysis (65-XX) 55 Optics, electromagnetic theory (78-XX) 53 Statistical mechanics, structure of matter (82-XX) 43 Quantum theory (81-XX) 33 Probability theory and stochastic processes (60-XX) 28 Operator theory (47-XX) 24 Mechanics of deformable solids (74-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 18 Mechanics of particles and systems (70-XX) 12 Global analysis, analysis on manifolds (58-XX) 12 Biology and other natural sciences (92-XX) 11 Difference and functional equations (39-XX) 10 Geophysics (86-XX) 7 Functional analysis (46-XX) 4 Real functions (26-XX) 4 Approximations and expansions (41-XX) 4 Integral equations (45-XX) 3 Combinatorics (05-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Systems theory; control (93-XX) 2 Measure and integration (28-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Integral transforms, operational calculus (44-XX) 1 Computer science (68-XX) Citations by Year