Oleg N. Kirillov has been a Research Fellow at the Magneto-Hydrodynamics Division of the Helmholtz-Zentrum Dresden-Rossendorf in Germany since 2011. His research interests include non-conservative stability problems of structural mechanics and physics, perturbation theory of non-self-adjoint boundary eigenvalue problems, magnetohydrodynamics, friction-induced oscillations, dissipation-induced instabilities and non-Hermitian problems of optics and microwave physics. Since 2013 he has served as an Associate Editor for the journal Frontiers in Mathematical Physics.Dmitry E. Pelinovsky has been Professor at McMaster University in Canada since 2000. His research profile includes work with nonlinear partial differential equations, discrete dynamical systems, spectral theory, integrable systems, and numerical analysis. He served as the guest editor of the special issue of the journals Chaos in 2005 and Applicable Analysis in 2010. He is an Associate Editor of the journal Communications in Nonlinear Science and Numerical Simulations.

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

Oleg N. Kirillov has been a Research Fellow at the Magneto-Hydrodynamics Division of the Helmholtz-Zentrum Dresden-Rossendorf in Germany since 2011. His research interests include non-conservative stability problems of structural mechanics and physics, perturbation theory of non-self-adjoint boundary eigenvalue problems, magnetohydrodynamics, friction-induced oscillations, dissipation-induced instabilities and non-Hermitian problems of optics and microwave physics. Since 2013 he has served as an Associate Editor for the journal Frontiers in Mathematical Physics.Dmitry E. Pelinovsky has been Professor at McMaster University in Canada since 2000. His research profile includes work with nonlinear partial differential equations, discrete dynamical systems, spectral theory, integrable systems, and numerical analysis. He served as the guest editor of the special issue of the journals Chaos in 2005 and Applicable Analysis in 2010. He is an Associate Editor of the journal Communications in Nonlinear Science and Numerical Simulations.

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

Oleg N. Kirillov has been a Research Fellow at the Magneto-Hydrodynamics Division of the Helmholtz-Zentrum Dresden-Rossendorf in Germany since 2011. His research interests include non-conservative stability problems of structural mechanics and physics, perturbation theory of non-self-adjoint boundary eigenvalue problems, magnetohydrodynamics, friction-induced oscillations, dissipation-induced instabilities and non-Hermitian problems of optics and microwave physics. Since 2013 he has served as an Associate Editor for the journal Frontiers in Mathematical Physics.Dmitry E. Pelinovsky has been Professor at McMaster University in Canada since 2000. His research profile includes work with nonlinear partial differential equations, discrete dynamical systems, spectral theory, integrable systems, and numerical analysis. He served as the guest editor of the special issue of the journals Chaos in 2005 and Applicable Analysis in 2010. He is an Associate Editor of the journal Communications in Nonlinear Science and Numerical Simulations.

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