Publication list for Schneider, Guido

Publication list for Schneider, Guido

  • The Dynamics of Modulated Wave Trains
    Base Product Code Keyword List: memo; MEMO; memo/199; MEMO/199; memo-199; MEMO-199; memo/199/934; MEMO/199/934; memo-199-934; MEMO-199-934
    Print Product Code: MEMO/199/934
    Online Product Code: MEMO/199/934.E
    Title (HTML): The Dynamics of Modulated Wave Trains
    Author(s) (Product display): Arjen Doelman; Björn Sandstede; Arnd Scheel; Guido Schneider
    Affiliation(s) (HTML): CWI, Amsterdam, The Netherlands; University of Surrey, Guildford, United Kingdom; University of Minnesota, Minneapolis, MN; Universität Stuttgart, Stuttgart, Germany
    Abstract:

    The authors investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg–Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number.

    The speed of these shocks is determined by the Rankine–Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh–Nagumo equation and to hydrodynamic stability problems.

    Book Series Name: Memoirs of the American Mathematical Society
    Publication Month and Year: 2009-04-10
    Copyright Year: 2009
    Page Count: 105
    Cover Type: Softcover
    Print ISBN-13: 978-0-8218-4293-5
    Online ISBN 13: 978-1-4704-0540-3
    Print ISSN: 0065-9266
    Online ISSN: 0065-9266
    Primary MSC: 35; 37
    Textbook?: False
    Applied Math?: False
    Electronic Media?: False
    Apparel or Gift: False
    SXG Subject: DE
    Online Price 1 Label: List
    Online Price 1: 70.00
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    Online Price 2 Label: Individual Member
    Online Price 2: 42.00
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  • Nonlinear PDEs: A Dynamical Systems Approach
    Base Product Code Keyword List: gsm; GSM; gsm/182; GSM/182; gsm-182; GSM-182
    Print Product Code: GSM/182
    Online Product Code: GSM/182.E
    Title (HTML): Nonlinear PDEs: A Dynamical Systems Approach
    Author(s) (Product display): Guido Schneider; Hannes Uecker
    Affiliation(s) (HTML): Universität Stuttgart, Stuttgart, Germany; Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
    Abstract:

    This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs.

    The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given.

    The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.

    Book Series Name: Graduate Studies in Mathematics
    Volume: 182
    Copyright Year: 2017
    Page Count: 575
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-3613-1
    Online ISBN 13: 978-1-4704-4228-6
    Print ISSN: 1065-7339
    Online ISSN: 1065-7339
    Primary MSC: 35; 37
    Textbook?: true
    Applied Math?: true
    Home Page?: true
    Sample?: false
    Reference?: false
    Electronic Media?: false
    Apparel or Gift: false
    SXG Subject: DE
    Online Price 1 Label: List
    Online Price 1: 99.00
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    Online Price 2: 79.20
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    Print Outstock Reason: NYP
    Print Outstock Reason Avail Date: Expected publication date November 05, 2017
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    Readership:

    Graduate students and researchers interested in nonlinear dynamics of PDEs.

    Related Products: Partial Differential Equations Nonlinear Dispersive Equations Global Solutions of Nonlinear Schrödinger Equations The Water Waves Problem
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