| Title | : | Spectral and Dynamical Stability of Nonlinear Waves (Applied Mathematical Sciences) |
| Author | : | |
| Rating | : | 4.91 (319 Votes) |
| Asin | : | 1461469945 |
| Format Type | : | Hardcover |
| Number of Pages | : | 361 Pages |
| Publish Date | : | 2013-06-06 |
| Genre | : |
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.
Editorial : From the book reviews:
“This 368-page book provides an excellent introduction to the spectral and nonlinear stability theory of nonlinear waves in one-dimensional domains. It is aimed primarily at graduate students, but it can certainly also be used by postdocs and other researchers who are interested in learning more about this area. … this book covers a broad range of topics in an area for which not many alternatives exist: the book is, in my opinion, an excellent addition to the literature.” (Bjorn Sandstede, Dynamical Systems Magazine, dynamicalsystems, April, 2014)
“The book under review focuses on stability of the equilibria of evolution equations. … The book consists of two parts. … Each chapter contains exercises, bibliographic comments and additional reading information. The reviewer evaluates the book as a significant achievement and recommends it to all interested readers.” (Radu Precup, zbMATH, Vol. 1297, 2014)<
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