Description
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 Schrodinger 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.
About the Author
Guido Schneider, Universitat Stuttgart, Germany.
Hannes Uecker, Carl von Ossietzky Universitat Oldenburg, Germany.
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
Book Information
ISBN 9781470436131
Author Guido Schneider
Format Hardback
Page Count 575
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 1160g
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 Schrodinger 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.
About the Author
Guido Schneider, Universitat Stuttgart, Germany.
Hannes Uecker, Carl von Ossietzky Universitat Oldenburg, Germany.
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
Book Information
ISBN 9781470436131
Author Guido Schneider
Format Hardback
Page Count 575
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 1160g
