Mechanism of State Transitions for the Vector Kuznetsov-Ma Breathers

Abstract

We study two types of mechanisms of state transitions for vector Kuznetsov-Ma breathers (KMBs) in the coupled Fokas-Lenells framework on unequal backgrounds. The amplitude imbalance breaks spectral reflection symmetry and generates richer breather morphologies. In the degenerate sector, KMBs approaching a non-self-conjugate degeneration curve from opposite sides yield different limiting solitons, revealing a discontinuous KMB-to-soliton transition. In the nondegenerate sector, the background plane waves become frequency matched at a special wavenumber, converting the KMB into a single- or two-soliton state. We determine the exact transition threshold and characterize how nearby solutions vary with the parameter. We further investigate special limiting mechanisms arising on the self-conjugate degeneration curve and on the real spectrum at the state-transition wavenumber. Numerical excitation provides further evidence for these results.