Stability of Nonlinear Waves in Hamiltonian Dynamial Systems

Anna Geyer, Dmitry E. Pelinovsky

$312

Paperback

Forthcoming
Pre-Order now

QTY:

English

American Mathematical Society
16 July 2025

Calculus & mathematical analysis; Applied mathematics; Mathematical physics

Series: Mathematical Surveys and Monographs

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.

By: Anna Geyer, Dmitry E. Pelinovsky
Imprint: American Mathematical Society
Country of Publication: United States
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9781470475529
ISBN 10: 1470475529
Series: Mathematical Surveys and Monographs
Pages: 380
Publication Date: 16 July 2025
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Forthcoming

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

Anna Geyer, Delft University of Technology, The Netherlands. Dmitry E. Pelinovsky, McMaster University, Hamilton, ON, Canada.