Download book Spectral and Dynamical Stability of Nonlinear Waves
Download book Spectral and Dynamical Stability of Nonlinear Waves
Spectral and Dynamical Stability of Nonlinear Waves.cKeith Promislow
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Author: Keith Promislow
Page Count: 374 pages
Published Date: 17 Jun 2013
Publisher: Springer-Verlag New York Inc.
Publication Country: New York, NY, United States
Language: English
ISBN: 9781461469940
Download Link: Spectral and Dynamical Stability of Nonlinear Waves
---------------------------------------------------------------
This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.
Read online Spectral and Dynamical Stability of Nonlinear Waves Buy Spectral and Dynamical Stability of Nonlinear Waves Download Spectral and Dynamical Stability of Nonlinear Waves for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook Spectral and Dynamical Stability of Nonlinear Waves
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Spectral and Dynamical Stability of Nonlinear Waves.cKeith Promislow
Author: Keith Promislow
Page Count: 374 pages
Published Date: 17 Jun 2013
Publisher: Springer-Verlag New York Inc.
Publication Country: New York, NY, United States
Language: English
ISBN: 9781461469940
Download Link: Spectral and Dynamical Stability of Nonlinear Waves
---------------------------------------------------------------
This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.
Read online Spectral and Dynamical Stability of Nonlinear Waves Buy Spectral and Dynamical Stability of Nonlinear Waves Download Spectral and Dynamical Stability of Nonlinear Waves for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook Spectral and Dynamical Stability of Nonlinear Waves
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