Nonlinear Physical Systems : Spectral Analysis, Stability and Bifurcations (Hardcover)

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