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Nonlinear evolution of the modulational instability and chaos using one-dimensional Zakharov equations and a simplified model
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10.1063/1.1850477
/content/aip/journal/pop/12/2/10.1063/1.1850477
http://aip.metastore.ingenta.com/content/aip/journal/pop/12/2/10.1063/1.1850477
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(a) 3D field plot of the electric field for Zakharov equations solved numerically for the initial condition [Eq. (2)] with . (b) 3D field plot of the electric field for Zakharov equations solved numerically for the initial condition [Eq. (2)] with . (c) 3D field plot of the electric field for Zakharov equations solved numerically for the initial condition [Eq. (2)] with .

Image of FIG. 2.
FIG. 2.

Time evolution of the absolute value of the maximum electric field corresponding to initial conditions as in Fig. 1(a) which illustrates a break up of periodicity.

Image of FIG. 3.
FIG. 3.

Time evolution of the absolute value of the Fourier components corresponding to Fig. 1(a) for (upper curve) and (lower curve).

Image of FIG. 4.
FIG. 4.

Time evolution of the absolute value of the Fourier component of the density when the electric field is evolving as in Fig. 1(a) (solid curve) and for (dash-dot curve) (Zakharov model).

Image of FIG. 5.
FIG. 5.

(a) Phase space plot in adiabatic case when , using simplified model. Plasmon number . (b) Phase space plot in adiabatic case when , using simplified model. Plasmon number .

Image of FIG. 6.
FIG. 6.

Time evolution of the absolute value of the Fourier component of the density for , using simplified model.

Image of FIG. 7.
FIG. 7.

Time evolution of the absolute value of the Fourier component for (upper curve) and (lower curve) when , using simplified model.

Image of FIG. 8.
FIG. 8.

Time evolution of the absolute value of the maximum electric field when , using simplified model.

Image of FIG. 9.
FIG. 9.

Phase space plot using simplified model in the nonadiabatic case when .

Image of FIG. 10.
FIG. 10.

3D spatiotemporal evolution of the field with contour plot showing periodic recurrence for through the Zakharov model.

Image of FIG. 11.
FIG. 11.

Contours of for through the Zakharov model showing localized patterns with slightly different structures.

Image of FIG. 12.
FIG. 12.

3D spatiotemporal evolution of the field for through the Zakharov model showing irregular spatially localized patterns that are still kept in the propagating process. This feature clearly illustrates the feature of spatial patterns that follow temporal chaos.

Image of FIG. 13.
FIG. 13.

(a) Lyapunov exponent vs wave number. (b) Lyapunov exponent vs wave number: Detailed view.

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/content/aip/journal/pop/12/2/10.1063/1.1850477
2005-01-25
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonlinear evolution of the modulational instability and chaos using one-dimensional Zakharov equations and a simplified model
http://aip.metastore.ingenta.com/content/aip/journal/pop/12/2/10.1063/1.1850477
10.1063/1.1850477
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