Full nonlinear evolution of modulation instability in the model of long wave-short wave resonance: spectral recurrence, two types of breathers, and their excitation
Phys. Rev. E 113, 054210 – Published 11 May, 2026
DOI: https://doi.org/10.1103/jtfd-ndtk
Abstract
The nonlinear stage of modulation instability (MI) starting with either purely periodic or localized periodic modulation is investigated analytically and numerically in the model of long wave-short wave (LS) resonance. Exact multiparametric solutions of Akhmediev breathers (ABs) and super-regular breathers (SRBs) are constructed based on an eigenvalue analysis. Physical spectra of ABs in analytic form are derived. The spectra of the short-wave component show expansion of energy from a single component to the sidebands and recurrence back to the same mode. However, the long-wave component shows complex oscillations in the sidebands, but the central mode remains constant. The evolution of LS-resonance-induced SRB is studied through its exact link with the MI. Our predictions based on exact analytical equations are confirmed by direct numerical simulations. We show that even nonideal single-wave excitations may lead asymptotically to the exact solutions. The connection of our exact solutions with results for the nonintegrable LS resonance model is also considered.
