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Nonlinear Physical Systems: Spectral Analysis, Sta bility and Bifurcations
Spectral Analysis, Stability and Bifurcations
ON Kirillov (Author)
9781848214200, Wiley
Hardback, published 29 November 2013
448 pages
23.9 x 16.2 x 2.9 cm, 0.802 kg
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems. Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynamics, and dissipation-induced instabilities are treated with the use of the theory of Krein and Pontryagin space, index theory, the theory of multi-parameter eigenvalue problems and modern asymptotic and perturbative approaches. Each chapter contains mechanical and physical examples, and the combination of advanced material and more tutorial elements makes this book attractive for both experts and non-specialists keen to expand their knowledge on modern methods and trends in stability theory.
Preface xiii Chapter 1. Surprising Instabilities of Simple Elastic Structures 1 Chapter 2. WKB Solutions Near an Unstable Equilibrium and Applications 15 Chapter 3. The Sign Exchange Bifurcation in a Family of Linear Hamiltonian Systems 41 Chapter 4. Dissipation Effect on Local and Global Fluid-Elastic Instabilities 67 Chapter 5. Tunneling, Librations and Normal Forms in a Quantum Double Well with a Magnetic Field 85 Chapter 6. Stability of Dipole Gap Solitons in Two-Dimensional Lattice Potentials 111 Chapter 7. Representation of Wave Energy of a Rotating Flow in Terms of the Dispersion Relation 139 Chapter 8. Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Chapter 9. Index Theorems for Polynomial Pencils 177 Chapter 10. Investigating Stability and Finding New Solutions in Conservative Fluid Flows Through Bifurcation Approaches 203 Chapter 11. Evolution Equations for Finite Amplitude Waves in Parallel Shear Flows 223 Chapter 12. Continuum Hamiltonian Hopf Bifurcation I 247 Chapter 13. Continuum Hamiltonian Hopf Bifurcation II 283 Chapter 14. Energy Stability Analysis for a Hybrid Fluid-Kinetic Plasma Model 311 Chapter 15. Accurate Estimates for the Exponential Decay of Semigroups with Non-Self-Adjoint Generators 331 Chapter 16. Stability Optimization for Polynomials and Matrices 351 Chapter 17. Spectral Stability of Nonlinear Waves in KdV-Type Evolution Equations 377 Chapter 18. Unfreezing Casimir Invariants: Singular Perturbations Giving Rise to Forbidden List of Authors 421 Index 425
Davide BIGONI, Diego MISSERONI, Giovanni NOSELLI and Daniele ZACCARIA
Jean-François BONY, Setsuro FUJIIÉ, Thierry RAMOND and Maher ZERZERI
Richard CUSHMAN, Johnathan M. ROBBINS and Dimitrii SADOVSKII
Olivier DOARÉ
Sergey Y. DOBROKHOTOV and Anatoly Y. ANIKIN
Nir DROR and Boris A. MALOMED
Yasuhide FUKUMOTO, Makoto HIROTA and Youichi MIE
Resonance 155
Igor HOVEIJN and Oleg N. KIRILLOV
Richard KOLLÁR and Radomír BOSÁK
Paolo LUZZATTO-FEGIZ and Charles H.K. WILLIAMSON
Sherwin A. MASLOWE
Philip J. MORRISON and George I. HAGSTROM
George I. HAGSTROM and Philip J. MORRISON
Philip J. MORRISON, Emanuele TASSI and Cesare TRONCI
Francis NIER
Michael L. OVERTON
Dmitry E. PELINOVSKY
Instabilities 401
Subject Areas: Mathematical modelling [PBWH]
