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Nonlinear PDEs: A Dynamical Systems Approach

Guido Schneider Universität Stuttgart, Stuttgart, Germany
Hannes Uecker Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
Available Formats:
Hardcover ISBN: 978-1-4704-3613-1
Product Code: GSM/182
List Price: $99.00 MAA Member Price:$89.10
AMS Member Price: $79.20 Electronic ISBN: 978-1-4704-4228-6 Product Code: GSM/182.E List Price:$99.00
MAA Member Price: $89.10 AMS Member Price:$79.20
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List Price: $148.50 MAA Member Price:$133.65
AMS Member Price: $118.80 Click above image for expanded view Nonlinear PDEs: A Dynamical Systems Approach Guido Schneider Universität Stuttgart, Stuttgart, Germany Hannes Uecker Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany Available Formats:  Hardcover ISBN: 978-1-4704-3613-1 Product Code: GSM/182  List Price:$99.00 MAA Member Price: $89.10 AMS Member Price:$79.20
 Electronic ISBN: 978-1-4704-4228-6 Product Code: GSM/182.E
 List Price: $99.00 MAA Member Price:$89.10 AMS Member Price: $79.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$148.50 MAA Member Price: $133.65 AMS Member Price:$118.80
• Book Details

Volume: 1822017; 575 pp
MSC: Primary 35; 37;

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.

Graduate students and researchers interested in nonlinear dynamics of PDEs.

• Chapters
• Introduction
• Basic ODE dynamics
• Dissipative dynamics
• Hamiltonian dynamics
• PDEs on an interval
• The Navier-Stokes equations
• Some dissipative PDE models
• Three canonical modular equations
• Reaction-diffusion systems
• Dynamics of pattern and the GL equation
• Wave packets and the NLS equation
• Long waves and their modular equations
• Center manifold reduction and spatial dynamics
• Diffusive stability

• Reviews

• This book as a whole is more than the sum of its chapters and deserves being slowly and thoughtfully read from the beginning to the end.

Michael Zaks, Mathematical Reviews
• This is an excellent text which can be used for several graduate courses in mathematics departments.

Dmitry Pelinovsky, Zentralblatt MATH
• The combination of rigor with simultaneous attention to associated real physical systems makes it particularly appealing.

William Satzer, MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1822017; 575 pp
MSC: Primary 35; 37;

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.

Graduate students and researchers interested in nonlinear dynamics of PDEs.

• Chapters
• Introduction
• Basic ODE dynamics
• Dissipative dynamics
• Hamiltonian dynamics
• PDEs on an interval
• The Navier-Stokes equations
• Some dissipative PDE models
• Three canonical modular equations
• Reaction-diffusion systems
• Dynamics of pattern and the GL equation
• Wave packets and the NLS equation
• Long waves and their modular equations
• Center manifold reduction and spatial dynamics
• Diffusive stability
• This book as a whole is more than the sum of its chapters and deserves being slowly and thoughtfully read from the beginning to the end.

Michael Zaks, Mathematical Reviews
• This is an excellent text which can be used for several graduate courses in mathematics departments.

Dmitry Pelinovsky, Zentralblatt MATH
• The combination of rigor with simultaneous attention to associated real physical systems makes it particularly appealing.

William Satzer, MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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