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.
Table of Contents:
Preface xiii
Chapter 1. Surprising Instabilities of Simple Elastic Structures 1
Davide BIGONI, Diego MISSERONI, Giovanni NOSELLI and Daniele ZACCARIA
Chapter 2. WKB Solutions Near an Unstable Equilibrium and Applications 15
Jean-François BONY, Setsuro FUJIIÉ, Thierry RAMOND and Maher ZERZERI
Chapter 3. The Sign Exchange Bifurcation in a Family of Linear Hamiltonian Systems 41
Richard CUSHMAN, Johnathan M. ROBBINS and Dimitrii SADOVSKII
Chapter 4. Dissipation Effect on Local and Global Fluid-Elastic Instabilities 67
Olivier DOARÉ
Chapter 5. Tunneling, Librations and Normal Forms in a Quantum Double Well with a Magnetic Field 85
Sergey Y. DOBROKHOTOV and Anatoly Y. ANIKIN
Chapter 6. Stability of Dipole Gap Solitons in Two-Dimensional Lattice Potentials 111
Nir DROR and Boris A. MALOMED
Chapter 7. Representation of Wave Energy of a Rotating Flow in Terms of the Dispersion Relation 139
Yasuhide FUKUMOTO, Makoto HIROTA and Youichi MIE
Chapter 8. Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1
Resonance 155
Igor HOVEIJN and Oleg N. KIRILLOV
Chapter 9. Index Theorems for Polynomial Pencils 177
Richard KOLLÁR and Radomír BOSÁK
Chapter 10. Investigating Stability and Finding New Solutions in Conservative Fluid Flows Through Bifurcation Approaches 203
Paolo LUZZATTO-FEGIZ and Charles H.K. WILLIAMSON
Chapter 11. Evolution Equations for Finite Amplitude Waves in Parallel Shear Flows 223
Sherwin A. MASLOWE
Chapter 12. Continuum Hamiltonian Hopf Bifurcation I 247
Philip J. MORRISON and George I. HAGSTROM
Chapter 13. Continuum Hamiltonian Hopf Bifurcation II 283
George I. HAGSTROM and Philip J. MORRISON
Chapter 14. Energy Stability Analysis for a Hybrid Fluid-Kinetic Plasma Model 311
Philip J. MORRISON, Emanuele TASSI and Cesare TRONCI
Chapter 15. Accurate Estimates for the Exponential Decay of Semigroups with Non-Self-Adjoint Generators 331
Francis NIER
Chapter 16. Stability Optimization for Polynomials and Matrices 351
Michael L. OVERTON
Chapter 17. Spectral Stability of Nonlinear Waves in KdV-Type Evolution Equations 377
Dmitry E. PELINOVSKY
Chapter 18. Unfreezing Casimir Invariants: Singular Perturbations Giving Rise to Forbidden
Instabilities 401
List of Authors 421
Index 425
