Edge bifurcations for near integrable systems via evans function techniques

SIAM Journal on Mathematical Analysis

Volumn 33, Issue 5, 2002, Pages 1117-1143

  Kapitula, Todd ^a   Sandstede, Björn ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Evans function; Inverse scattering theory; Stability; Travelling waves

Indexed keywords

EID: 0036373932     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141000372301     Document Type: Article

References (40)

1. Solitons, nonlinear evolution equations, and inverse scattering
2. The inverse scattering transform-Fourier analysis for nonlinear problems
3. A topological invariant arising in the stability of travelling waves
4. Vibrations and oscillatory instabilities of gap solitons
5. Nerve axon equations I: Linear approximations
6. Nerve axon equations II: Stability at rest
7. Nerve axon equations III: Stability of the nerve impulse
8. Nerve axon equations IV: The stable and unstable impulse
9. The gap lemma and geometric criteria for instability of viscous shock profiles
10. Geometric theory of semilinear parabolic equations
11. Stability criterion for bright solitary waves of the perturbed cubic-quintic Schrödinger equation
12. The evans function and generalized melnikov integrals
13. Stability of waves in perturbed Hamiltonian systems
14. Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
15. Instability mechanism for bright solitary-wave solutions to the cubic-quintic Ginzburg-Landau equation
16. Stability of bright solitary wave solutions to perturbed non-linear Schrödinger equations
17. Closure of the squared Zakharov Shabat eigenstates
18. A perturbation expansion for the Zakharov-Shabat inverse scattering transform
19. Perturbation theory for solitons in optical fibers
20. The squared eigenfanctions of the massive Thirring model in laboratory coordinates
21. Variational method: How it can create false instabilities
22. Evolution equations, singular dispersion relations, and moving eigenvalues
23. Internal modes of solitary waves
24. Soliton stability and interactions in fibre lasers
25. The mechanism of the polarizational mode instability in birefringent fiber optics
26. Vibration modes of a gap soliton in a nonlinear optical medium
27. The inverse scattering transform
28. Eigenvalues, and instabilities of solitary waves
29. Internal modes of envelope solitons
30. Bifurcations of new eigenvalues for the Benjamin-Ono equation
31. Eigenfunctions and eigenvalues for a scalar Riemann-Hilbert problem associated to inverse scattering
32. Stability, multistability, and wobbling of optical gap solitons
33. Fronts, pulses, sources, and sinks in the generalized complex Ginzburg-Landau equation
34. Stability of travelling waves
35. Resonance Thirring solitons in type II second-harmonic generation
36. Modulational stability of ground states of nonlinear Schrödinger equations
37. Stability and evolution of solitary waves in perturbed generalized nonlinear Schrödinger equations