Homoclinic orbits and chaos in a second-harmonic generating optical cavity

Aceves, Alejandro B.; Holm, Darryl D.; Kovačič, Gregor; Timofeyev, Ilya

doi:10.1016/s0375-9601(97)00468-4

Search citation statements

Order By: Relevance

Paper Sections

Select...

Equations Of Motion1

The Project's First Year --New Wave Mean-flow Interaction (1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1999

2017

Publication Types

Select...

Article2

Other1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Wersinger, Finn, and Ott [29] used a forced and damped version of the three-wave equations to study instability saturation by nonlinear mode coupling and found irregular solutions indicating the presence of a strange attractor. See also [1,12,13,24] for more detailed studies of the perturbed three-wave system.…”

Section: Equations Of Motionmentioning

confidence: 99%

Stepwise Precession of the Resonant Swinging Spring

Holm¹,

Lynch²

2002

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

Abstract. The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the well-known three-wave equations that also apply, for example, in laser-matter interaction in a cavity. We use Hamiltonian reduction and pattern evocation techniques to derive a formula that describes the characteristic feature of this system's dynamics, namely, the stepwise precession of its azimuthal angle.

show abstract

Section: Equations Of Motionmentioning

confidence: 99%

Stepwise Precession of the Resonant Swinging Spring

Holm¹,

Lynch²

2002

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

show abstract

“…We also found the relations of these results to the non-acceleration theorem [3], averaging [4,5], WKB 6 stability theory [6], and Lagrangian-mean fluid equations for prescribed wave displacements such as those of [7]. Poincm6 for dynamics on a Lie algebra, in that they depend on a parameter and this parameter in fluid dynamics applications has the interpretation of being advected, or Lie dragged, as with the density in compressible fluid flow.…”

Section: The Project's First Year --New Wave Mean-flow Interaction (mentioning

confidence: 99%