Multiple-period dispersion-managed solitons

We present a class of solutions with a period multiple to that one of the standard dispersion-managed soliton in the nonlinear Schrödinger equation with periodic variations of dispersion.

Figure 1

The dependence of minimal $T$ on dimensionless energy $c$. Thin lines represent the simple periodic solutions with several values of $\overline{d}$: they correspond, from upper to lower, to $\overline{d}=0.1,0.03,0,-0.01,-0.03$. Thick lines represent multiple period solutions with $\overline{d}=0.1$; the solid line, the line with long dashes, and the line with short dashes correspond, respectively, to $n=10$, 6, and 4.

Figure 2

The trajectories of the points on the $(T,M)$ plane under $g^m$ for $c=3.5$, $\overline{d}=0$.

Figure 3

Evolution of $T$ and $M$ for a single period DM soliton (the upper two plots) and four-period solution (the lower two plots). Here $c=3.94$, $\overline{d}=0.03$, and $d_1=\mid d_2\mid =L=1$.

Figure 4

Dependence of the normalized average power $N_{\mathrm{norm}}^2$ on map strength $S$. The plot $A$ represents the simple periodic solutions with $\overline{d}=0.1,0,-0.03$. On the plot $B$ the same simple periodic solutions are compared to multiple-period solutions (thick lines). The solid, long-dashed, and short-dashed thick lines correspond, respectively, to $n=10$, 6, and 4.