Stability of Nonlinear Waves in Hamilton
Anna Geyer; Dmitry E. Pelinovsky
ISBN 10: 1470475529 ISBN 13: 9781470475529
Published by American Mathematical Society, 2025
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Synopsis:
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.
About the Author:
Anna Geyer, Delft University of Technology, The Netherlands.
Dmitry E. Pelinovsky, McMaster University, Hamilton, ON, Canada.
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Bibliographic Details
Title: Stability of Nonlinear Waves in Hamilton
Publisher: American Mathematical Society
Publication Date: 2025
Binding: Soft cover
Condition: As New