Abstract
We study the stabilization of nonchaotic periodic and quasi-periodic
solutions of both integrable (α=1) and nonintegrable
(α=2/3) of CCNLS equations of the form:
\begin{eqnarray*}
ip_t +p_{xx} +\frac{1}{2} \sigma (| p |^2 +\alpha | q |^2) p &= & \gamma
g_1 (x)\exp (-i\omega_1t)\,,\\[5pt]
iq_t +q_{xx} +\frac{1}{2} \sigma (\alpha | p |^2 +| q |^2) q &= &
\gamma g_2 (x)\exp (-i\omega_2t)\,,
\end{eqnarray*}
where subscripts mean partial derivatives, p(x,t) and q(x,t)
are the orthogonal components of an electric field in a glass fiber,
$i=\sqrt{-1}$
,
the defocusing (σ=-1) and focusing (σ=1)
cases are distinguished by σ; g1(x) and g2(x) are periodic functions in x and γ; and ω1 and ω2 are parameters. These solutions do not
display sensitive dependence on initial conditions. The stabilization of
solutions are studied using a feedback control method and their maximal
Lyapunov exponents are calculated. Periodic solutions of this system are
important in the study of these coupled equations, since they represent
stationary or repeatable behavior.