Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in Nonlinear Schrödinger Equation

We show that the nonlinear stage of the dual-wavelength pumped modulation instability (MI) in nonlinear Schrödinger equation (NLSE) can be effectively analyzed by mode truncation methods. The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves. Significantly, the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories ran along the Hamiltonian contours of the heteroclinic structure. It is demonstrated that there is much richer dynamic behavior, in contrast to the nonlinear waves reported before. This novel nonlinear wave promises to inject new vitality into the study of MI.