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Mathematics

D-Index
34
Citations
3985
World Ranking
2950
National Ranking
181

Overview

Guido Schneider is affiliated with the University of Stuttgart in Germany and contributes extensively to the fields of Physics and Astronomy as well as Mathematics. Their research primarily focuses on areas intersecting statistical and nonlinear physics, mathematical physics, and applied mathematical problems.

The scientist's recent scholarly publications illustrate a concentration on nonlinear dynamics, modulation theory, and wave phenomena. Notable papers include:

  • "Failure of the N-wave interaction approximation without imposing periodic boundary conditions," published in 2020 in ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
  • "KP-II Approximation for a Scalar Fermi-Pasta-Ulam System on a 2D Square Lattice," published in 2023 in SIAM Journal on Applied Mathematics
  • "A proof of validity for multiphase Whitham modulation theory," published in 2020 in Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
  • "The amplitude system for a Simultaneous short-wave Turing and long-wave Hopf instability," published in 2021 in Discrete and Continuous Dynamical Systems - S
  • "Modulation Equations Near the Eckhaus Boundary: The KdV Equation," published in 2020 in SIAM Journal on Mathematical Analysis

Their frequent publication venues also include:

  • arXiv (Cornell University)
  • Lebensmittel Zeitung
  • SSRN Electronic Journal
  • Journal of Applied Analysis
  • Jahresbericht der Deutschen Mathematiker-Vereinigung

Guido Schneider's collaborations span several researchers with whom they have repeatedly worked on related topics. Frequent co-authors include:

  • Dmitry E. Pelinovsky
  • Björn de Rijk
  • Bastian Hilder
  • T. Haas
  • Nicole Gauß

The scientist's research topics broadly engage with nonlinear complex systems and differential equations. Key areas of scholarly emphasis are:

  • Nonlinear Photonic Systems
  • Advanced Mathematical Physics Problems
  • Nonlinear Waves and Solitons
  • Nonlinear Dynamics and Pattern Formation
  • Quantum chaos and dynamical systems
  • Stability and Controllability of Differential Equations
  • Numerical methods for differential equations

This body of work contributes to a deeper understanding of nonlinear effects in physical systems and mathematical structures, combining analytical and numerical approaches to problems in applied and theoretical physics.

Best Publications

  • The validity of modulation equations for extended systems with cubic nonlinearities

    Pius Kirrmann;Guido Schneider;Alexander Mielke

  • Attractors for modulation equations on unbounded domains-existence and comparison

    A Mielke;G Schneider

  • The long‐wave limit for the water wave problem I. The case of zero surface tension

    Guido Schneider;C. Eugene Wayne

  • The Dynamics of Modulated Wave Trains

    Arjen Doelman;Björn Sandstede;Arnd Scheel;Guido Schneider

  • DIFFUSIVE STABILITY OF SPATIAL PERIODIC SOLUTIONS OF THE SWIFT-HOHENBERG EQUATION

    Guido Schneider

  • Error estimates for the Ginzburg-Landau approximation

    Guido Schneider

  • The Rigorous Approximation of Long-Wavelength Capillary-Gravity Waves

    Guido Schneider;C. Eugene Wayne

  • Validity and Limitation of the Newell‐Whitehead Equation

    Guido Schneider

  • Justification of modulation equations for hyperbolic systems via normal forms

    Guido Schneider

  • Photonic Crystals: Mathematical Analysis and Numerical Approximation

    Willy Dörfler;Armin Lechleiter;Michael Plum;Guido Schneider

  • Nonlinear Stability of Taylor Vortices in Infinite Cylinders

    Guido Schneider

  • Kawahara dynamics in dispersive media

    Guido Schneider;C.Eugene Wayne

  • A new estimate for the Ginzburg-Landau approximation on the real axis

    Guido Schneider

  • Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances

    Guido Schneider

  • Propagation of hexagonal patterns near onset

    Arjen Doelman;Björn Sandstede;Arnd Scheel;Guido Schneider

  • On the validity of the variational approximation in discrete nonlinear Schrödinger equations

    Christopher Chong;Christopher Chong;Dmitry E. Pelinovsky;Dmitry E. Pelinovsky;Guido Schneider

  • Global existence via Ginzburg-Landau formalism and pseudo- orbits of Ginzburg-Landau approximations

    Guido Schneider

  • Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential

    Dmitry Pelinovsky;Guido Schneider

  • Bifurcations of Standing Localized Waves on Periodic Graphs

    Dmitry Pelinovsky;Guido Schneider

  • Justification of the nonlinear Schrödinger equation in spatially periodic media

    Kurt Busch;Guido Schneider;Lasha Tkeshelashvili;Hannes Uecker

  • KP description of unidirectional long waves. The model case

    Thierry Gallay;Guido Schneider

  • Nonlinear Pdes: A Dynamical Systems Approach

    Guido Schneider;Hannes Uecker

Frequent Co-Authors

Dmitry E. Pelinovsky
Dmitry E. Pelinovsky McMaster University
C. Eugene Wayne
C. Eugene Wayne Boston University
Björn Sandstede
Björn Sandstede Brown University
Arnd Scheel
Arnd Scheel University of Minnesota
Alexander Mielke
Alexander Mielke Weierstrass Institute for Applied Analysis and Stochastics
Jean-Pierre Eckmann
Jean-Pierre Eckmann University of Geneva
Arjen Doelman
Arjen Doelman Leiden University
Panayotis G. Kevrekidis
Panayotis G. Kevrekidis University of Massachusetts Amherst
Wolfgang Nowak
Wolfgang Nowak University of Stuttgart
Hans-Joachim Wunderlich
Hans-Joachim Wunderlich University of Stuttgart

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