Dynamics of Flat-Top Solitons under Dispersion Management

The dynamics of flat-top solitons in dispersion-managed systems are investigated using a variational approach applied to the cubic-quintic nonlinear Schrödinger equation. This study derives the effective Lagrangian and variational equations of motion, revealing the evolution of soliton parameters under time-dependent dispersion. Linear stability analysis around fixed points yields the natural frequency of perturbations, validated with specific parameter values. A reduced second-order width equation, possessing a Mathieu-type structure, is constructed and used to generate a parametric stability diagram that identifies resonance-induced instability regions. Direct comparisons with full variational and numerical simulations reveal the role of higher-order nonlinearities in suppressing unbounded growth, even within linearly unstable regimes. Results demonstrate the stability characteristics of flat-top solitons, offering insights into their behavior in nonlinear optical systems.