Generalized Maslov Indices for Non-Hamiltonian Systems

DOI10.1137/20M1381319zbMath1498.37023arXiv2006.14517OpenAlexW3199743147WikidataQ114074132 ScholiaQ114074132MaRDI QIDQ5065451

Graham Cox, Paul Cornwell, Robert Marangell, Christopher K. R. T. Jones, Thomas John Baird

Publication date: 21 March 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.14517

zbMATH Keywords

stabilityreaction-diffusion systemsMaslov indexnon-Hamiltonian systems

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Lagrangian submanifolds; Maslov index (53D12) Index theory for dynamical systems, Morse-Conley indices (37B30) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51)

Related Items (4)

Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation ⋮ A generalized index theory for non-Hamiltonian system ⋮ The Maslov index and spectral counts for linear Hamiltonian systems on \(\mathbb{R}\) ⋮ Renormalized oscillation theory for regular linear non-Hamiltonian systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An instability criterion for nonlinear standing waves on nonzero backgrounds
• Computing the Maslov index of solitary waves. II: Phase space with dimension greater than four
• Computing the Maslov index of solitary waves. I: Hamiltonian systems on a four-dimensional phase space
• The Maslov index for paths
• Absolute and convective instabilities of waves on unbounded and large bounded domains
• Mini-maximizers for reaction-diffusion systems with skew-gradient structure
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• The Maslov index for Lagrangian pairs on \(\mathbb{R}^{2 n}\)
• Stability analysis for standing pulse solutions to FitzHugh-Nagumo equations
• Maslov index for homoclinic orbits of Hamiltonian systems
• Instability of standing waves for non-linear Schrödinger-type equations
• Instability of pulses in gradient reaction–diffusion systems: a symplectic approach
• On the Existence and Stability of Fast Traveling Waves in a Doubly Diffusive FitzHugh--Nagumo System
• Rigorous Numerics in Dynamics
• The chemical basis of morphogenesis
• The Maslov and Morse indices for system Schroedinger operators on \mathBB{R}
• Clifford Algebras and Lie Theory
• Localized standing waves in inhomogeneous Schrödinger equations
• A stability index for travelling waves in activator-inhibitor systems
• Opening the Maslov box for traveling waves in skew-gradient systems: counting eigenvales and proving (in)stability
• Computing the Maslov index for large systems
• Transversality of homoclinic orbits, the Maslov index and the symplectic Evans function
• Standing pulse solutions in reaction-diffusion systems with skew-gradient structure

This page was built for publication: Generalized Maslov Indices for Non-Hamiltonian Systems