Stability of Nonlinear Waves in Hamiltonian Dynamial Systems
Seiten
2025
American Mathematical Society (Verlag)
978-1-4704-7552-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-7552-9 (ISBN)
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Dive into the rigorous study of stability in nonlinear waves within Hamiltonian systems, bridging classical equilibrium analysis with modern methods for infinite-dimensional dispersive equations. Explore techniques for orbital stability and linearization, alongside innovative approaches for challenging wave phenomena.
This monograph offers a comprehensive and accessible treatment of both classical and modern approaches to the stability analysis of nonlinear waves in Hamiltonian systems. Starting with a review of stability of equilibrium points and periodic orbits in finite-dimensional systems, it advances to the infinite-dimensional setting, addressing orbital stability and linearization techniques for spatially decaying and spatially periodic solutions of nonlinear dispersive wave equations, such as the nonlinear Schrodinger, Korteweg-de Vries, and Camassa-Holm equations. The book rigorously develops foundational tools, such as the Vakhitov-Kolokolov slope criterion, the Grillakis-Shatah-Strauss approach, and the integrability methods, but it also introduces innovative adaptations of the stability analysis in problems where conventional methods fall short, including instability of peaked traveling waves and stability of solitary waves over nonzero backgrounds. Aimed at graduate students and researchers, this monograph consolidates decades of research and presents recent advancements in the field, making it an indispensable resource for those studying the stability of nonlinear waves in Hamiltonian systems.
This monograph offers a comprehensive and accessible treatment of both classical and modern approaches to the stability analysis of nonlinear waves in Hamiltonian systems. Starting with a review of stability of equilibrium points and periodic orbits in finite-dimensional systems, it advances to the infinite-dimensional setting, addressing orbital stability and linearization techniques for spatially decaying and spatially periodic solutions of nonlinear dispersive wave equations, such as the nonlinear Schrodinger, Korteweg-de Vries, and Camassa-Holm equations. The book rigorously develops foundational tools, such as the Vakhitov-Kolokolov slope criterion, the Grillakis-Shatah-Strauss approach, and the integrability methods, but it also introduces innovative adaptations of the stability analysis in problems where conventional methods fall short, including instability of peaked traveling waves and stability of solitary waves over nonzero backgrounds. Aimed at graduate students and researchers, this monograph consolidates decades of research and presents recent advancements in the field, making it an indispensable resource for those studying the stability of nonlinear waves in Hamiltonian systems.
Anna Geyer, Delft University of Technology, The Netherlands. Dmitry E. Pelinovsky, McMaster University, Hamilton, ON, Canada.
Stability in finite-dimensional systems
Stability of solitary waves
Stability of periodic waves
Orbital stability in integrable Hamiltonian systems
Spectral stability in integrable Hamiltonian systems
Stability of peaked waves
Stability of domain walls and black solitons
Jacobi elliptic functions and integrals
Spectral theory for linear operators
Bibliography
Index
| Erscheinungsdatum | 02.08.2025 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-4704-7552-9 / 1470475529 |
| ISBN-13 | 978-1-4704-7552-9 / 9781470475529 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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