Dmitry E. Pelinovsky and Vadim Zharnitsky
Averaging of dispersion-managed pulses:
existence and stability
SIAM J. Appl. Math. 63, 745-776 (2003)
We consider existence and stability of dispersion-managed pulses
in the two approximations of the periodic NLS equation: (i) a dynamical
system for a Gaussian pulse and (ii) an average integral NLS
equation. We apply normal form transformations for
finite-dimensional and infinite-dimensional Hamiltonian systems
with periodic coefficients. First-order corrections to the leading-order
averaged Hamiltonian are derived explicitly for both approximations.
Bifurcations of pulse solutions and
their stability are studied by analysis of critical points
of the first-order averaged Hamiltonians. The validity of the
averaging procedure is verified and the presence of ground states
corresponding to dispersion-managed pulses in the averaged
Hamiltonian is established.
EXISTENCE AND STABILITY OF PULSES, OPTICAL SOLITONS,
DISPERSION MANAGEMENT, AVERAGING THEORY, NORMAL FORM TRANSFORMATIONS,
ERRORS and CONVERGENCE OF ASYMPTOTIC SERIES, PERIODIC NLS EQUATION,
INTEGRAL NLS EQUATIONS, GAUSSIAN APPROXIMATION.