Edge Bifurcations for Near Integrable Systems via Evans Function Techniques

DOI10.1137/S0036141000372301zbMath1092.37048OpenAlexW2088384142WikidataQ60143915 ScholiaQ60143915MaRDI QIDQ2782974

Björn Sandstede, Todd Kapitula

Publication date: 8 April 2002

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

Full work available at URL: https://doi.org/10.1137/s0036141000372301

zbMATH Keywords

stabilitytravelling wavesEvans functioninverse scattering theory

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) General topics in linear spectral theory for PDEs (35P05) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50)

Related Items

Nonlinear Eigenvalue Methods for Linear Pointwise Stability of Nonlinear Waves, Existence and stability of spatially localized patterns, Linear and orbital stability analysis for solitary-wave solutions of variable-coefficient scalar-field equations, Instability of local deformations of an elastic rod, Transverse instabilities of deep-water solitary waves, Computing Evans functions numerically via boundary-value problems, Orbital stability of Dirac solitons, Criteria for pointwise growth and their role in invasion processes, Spectral stability analysis for periodic traveling wave solutions of NLS and CGL perturbations, Evans functions, Jost functions, and Fredholm determinants, Asymptotic stability of solitary waves in generalized Gross-Neveu model, Integrability revisited: a necessary condition, Evaluating the Evans function: Order reduction in numerical methods, Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems, Stability and instability of nonlinear defect states in the coupled mode equations-analytical and numerical study, On spectral stability of the nonlinear Dirac equation, Parameterization Method for Unstable Manifolds of Standing Waves on the Line, Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity, Stability Analysis for Combustion Fronts Traveling in Hydraulically Resistant Porous Media, Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear Schrödinger problem, The parametrically modified sine-Gordon equation: Spectral properties, collisions, resonances and their connection to integrability, A degenerate edge bifurcation in the 1D linearized nonlinear Schrödinger equation, Travelling waves in a singularly perturbed sine-Gordon equation