FPTU recurrence within the Gardner equation

The study of Fermi–Pasta–Ulam–Tsingou (FPUT) recurrence is examined within the framework of the Gardner equation. The evolution of harmonic waves is investigated for both positive and negative cubic nonlinearities. It is observed that harmonic waves undergo fission into solitons, which then interact with each other. For positive cubic nonlinearity, recurrence occurs periodically over time for weak and intermediate nonlinearities. However, as the dispersion becomes weaker, this phenomenon ceases to occur. Conversely, for negative cubic nonlinearity, recurrence is also observed for weak and intermediate nonlinearities, but it lacks a well-defined temporal period.