ハミルトン力学系における非線形波動の安定性 8月22日刊行予定

◎書名：　Stability　of　Nonlinear　Waves　in　Hamiltonian　Dynamical　Systems
◎和名：　ハミルトン力学系における非線形波動の安定性　
◎ISBN：　978-1-4704-7552-9

●著者：Geyer,Anna/Pelinovsky,DmitryE
●出版社：American Mathematical Society
●ISBN：978-1-4704-7552-9
●刊行：2025/08
● paper/380P
●解析学




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.

ハミルトン系における非線形波動の安定性解析について、古典的な手法と現代的な手法の両方を包括的に解説。

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