Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation

Physica D: Nonlinear Phenomena

Volumn 162, Issue 3-4, 2002, Pages 155-187

  Higuera, M ^a,b   Porter, J ^b,c   Knobloch, E ^c,d  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b Northwestern University   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Global bifurcation; Nonlinear Schr dinger equation; Parametric instability

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; GALERKIN METHODS; PARTIAL DIFFERENTIAL EQUATIONS; SWITCHING; WAVE PROPAGATION;

HETEROCLINIC DYNAMICS; NONLINEAR SCHRODINGER EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0037084141     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00368-2     Document Type: Article

References (44)

1. Time-modulated oscillatory convection
2. Temporal modulation of travelling waves
3. Temporal forcing of small-amplitude waves in anisotropic systems
4. Temporal modulation of travelling waves in the flow between rotating cylinders with broken azimuthal symmetry
5. Parametrically forced surface waves
6. Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio
7. Dynamics of counterpropagating waves in parametrically forced systems
8. Amplitude equations for travelling wave convection
9. Coupled NLS equations for counter-propagating waves in systems with reflection symmetry
10. Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator
11. The effects of nonlocal interactions on the dynamics of the Ginzburg-Landau equation
12. Finite-dimensional behaviour for weakly damped driven Schrödinger equations
13. An energy equation for the weakly damped driven nonlinear Schrödinger equations and its application to their attractors
14. Regularity of attractor for a weakly damped nonlinear Schrödinger equation
15. Analyticity of the attractor and the number of determining modes for a weakly damped driven nonlinear Schrödinger equation
16. Finite-dimensional description of doubly diffusive convection
17. Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation
18. Global bifurcations into chaos in systems with SO(2) symmetry
19. Finite-dimensional models of the Ginzburg-Landau equation
20. A modal representation of chaotic attractors for the driven, damped pendulum chain
21. Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation
22. Orbits homoclinic to resonances: The Hamiltonian case
23. N-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems
24. Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schrödinger equation
25. Large-scale flow in turbulent convection: A mathematical model
26. Analysis of the shearing instability in nonlinear convection and magnetoconvection
27. Onset of zero Prandtl number convection
28. Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
29. Bifurcations in a model of double-diffusive convection
30. Local and global behavior near homoclinic orbits
31. Suppression of period doubling in symmetric systems
32. Bifurcations near homoclinic orbits with symmetry
33. About some theorems by L.P. Shil'nikov
34. From attractor to saddle: A tale of transverse instability
35. Bifocal homoclinic orbits in four dimensions
36. A possible new mechanism for the onset of turbulence
37. Two mechanisms of the transition to chaos in finite-dimensional models of convection
38. Homoclinic orbits in a four-dimensional model of a perturbed NLS equation: A geometric singular perturbation study
39. Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system