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A self-consistent three-wave coupling model with complex linear frequencies
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10.1063/1.3640807
/content/aip/journal/pop/18/9/10.1063/1.3640807
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/9/10.1063/1.3640807
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Stability diagram of Δω = −2.5 and Im ω1 = 0.3. The horizontal and vertical axes represent γ2 and γ3. The thick blue line (dashed) shows the stability condition Δγ = γ c  = 3Γ3/2Γ2 in Eq. (20). The thick red line (solid) shows Re σ = 0. Triad (I) (+), Triad (II) (Δ), and Triad (III) (⋄) are shown for Sec. IV.

Image of FIG. 2.
FIG. 2.

(Color online) The evolution of the mode energies (left) and the triad phase (right), from the numerical simulations of Eq. (1) for Triad (I). The black (solid), red (dotted), and blue (dashed) traces represent modes 1, 2, and 3. The red horizontal line indicates the triad phase of the fixed point, Δψ0.

Image of FIG. 3.
FIG. 3.

(Color online) The evolution of the mode energies (left) and the triad phase (right), from the numerical simulations of Eq. (1) for Triad (II) (top) and Triad (III) (bottom). The legends in the plots are described in Fig. 2.

Image of FIG. 4.
FIG. 4.

(Color online) Time evolution of three phases ψ i [black (+), red (*), blue (⋄)] and the triad phase Δψ [green (△)] of the unstable Triad (II) (left) and the stable Triad (III) (right) at t = 90−95.

Image of FIG. 5.
FIG. 5.

(Color online) The frequency spectra of the mode ψ1 (black, solid), the mode ψ2 (red, dotted) and the mode ψ3 (blue, dashed) are plotted at t = (a) 100, (b) 125, (c) 150, (d) 200, (e) 250. The vertical lines represent (black, solid), (red, dotted), (blue, dashed), σ f (green, long dash), and ωamp (black, dash dot). The arrows and the shaded region refer to the interval bounded by .

Image of FIG. 6.
FIG. 6.

(Color online) The evolution of (a) amplitudes φ i (b) the triad phase Δψ (c) n i (d) m i are shown with the initial condition of Ψ = Ψ0 and Δψ = −Δψ0. Black (solid), red (dotted), and blue (dashed) lines in (a,c,d) represent the modes i = 1, 2, 3.

Image of FIG. 7.
FIG. 7.

(Color online) ((a) and (b)) The frequency spectra at t = 0,75 in Fig. 6(c) (Re φ1, Im φ1) at t = 0,75. The legends for the spectra are the same as in Fig. 5 and the red dashed line in (c) and (d) represent the mode 1 at the fixed point.

Image of FIG. 8.
FIG. 8.

(Color online) [β = i] (a and d) Φ i (b and e) Δψ and (c and f) the frequency spectra at t = 325(c) and 200(f). The top panel (a, b, c) and the bottom panel (d, e, f) corresponds to the strength of the perturbation f 0 = 0.1 and f 0 = 0.5. Each plot has the same legends as described in Figs. 2 and 5.

Image of FIG. 9.
FIG. 9.

(Color online) [β = 1] (a and d) Φ i (b and e) Δψ and (c and f) the frequency spectra at t = 325. The top panel (a, b, c) and the bottom panel (d, e, f) corresponds to the strength of the perturbation f 0 = 0.1 and f 0 = 0.2. Each plot has the same legends as described in Figs. 2 and 5.

Image of FIG. 10.
FIG. 10.

(Color online) Diagram of two triad connection.

Image of FIG. 11.
FIG. 11.

(Color online) In the case of tan Δψ1 = tan Δψ2 and σ1 < σ2, the amplitudes of (a) the modes 1 (black, solid), 2 (red, dotted), 3 (blue, dashed) of triad 1 and (b) the modes 1′ (black, solid), 2′ (red, dotted), 3′ (blue, dashed) of triad 2 are shown in time.

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/content/aip/journal/pop/18/9/10.1063/1.3640807
2011-09-30
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A self-consistent three-wave coupling model with complex linear frequencies
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/9/10.1063/1.3640807
10.1063/1.3640807
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