Opening the Maslov box for traveling waves in skew-gradient systems: counting eigenvales and proving (in)stability
From MaRDI portal
Publication:5113786
DOI10.1512/iumj.2019.68.7831zbMath1442.35208arXiv1709.01908OpenAlexW4243513657WikidataQ126567614 ScholiaQ126567614MaRDI QIDQ5113786
Publication date: 17 June 2020
Published in: Indiana University Mathematics Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1709.01908
Reaction-diffusion equations (35K57) Traveling wave solutions (35C07) Semilinear parabolic equations (35K58)
Related Items
Exponential dichotomies for nonlocal differential operators with infinite range interactions ⋮ Maslov index for heteroclinic orbits of non-Hamiltonian systems on a two-dimensional phase space ⋮ Generalized Maslov Indices for Non-Hamiltonian Systems ⋮ Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation ⋮ Simple and multiple traveling waves in a reaction-diffusion-mechanics model ⋮ The Maslov index and spectral counts for linear Hamiltonian systems on \(\mathbb{R}\) ⋮ Bifurcation to instability through the lens of the Maslov index ⋮ Stability of Traveling Waves for Reaction-Diffusion Equations with Multiplicative Noise ⋮ Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations ⋮ Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions ⋮ A stability index for travelling waves in activator-inhibitor systems ⋮ Index theory for traveling waves in reaction diffusion systems with skew gradient structure ⋮ Stability of traveling wave in a PDE approximation of coupled arrays of Chua's circuit
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Traveling pulse solutions to Fitzhugh-Nagumo equations
- Stability of travelling front solutions of the FitzHugh-Nagumo equations
- Computing the Maslov index of solitary waves. II: Phase space with dimension greater than four
- Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations
- Geometric theory of semilinear parabolic equations
- The Maslov index for paths
- Mini-maximizers for reaction-diffusion systems with skew-gradient structure
- Mathematical biology. Vol. 2: Spatial models and biomedical applications.
- Spectral and dynamical stability of nonlinear waves
- The Maslov and Morse indices for Schrödinger operators on \([0,1\)]
- Stability analysis for standing pulse solutions to FitzHugh-Nagumo equations
- Maslov index for homoclinic orbits of Hamiltonian systems
- Counting spectrum via the Maslov index for one dimensional $\theta -$periodic Schrödinger operators
- Stability Analysis for the Slow Travelling Pulse of the FitzHugh–Nagumo System
- Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
- Instability of standing waves for non-linear Schrödinger-type equations
- Spectral asymmetry and Riemannian geometry. III
- 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
- The Maslov and Morse indices for system Schroedinger operators on \mathBB{R}
- Unstable eigenvalues and the linearization about solitary waves and fronts with symmetry
- Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium
- Stability of the in-phase travelling wave solutions in a pair of coupled nerve fibers
- The Morse and Maslov indices for matrix Hill's equations
- Transversality of homoclinic orbits, the Maslov index and the symplectic Evans function
- The symplectic Evans matrix, and the instability of solitary waves and fronts
- Standing pulse solutions in reaction-diffusion systems with skew-gradient structure
