Novel Transition Mechanisms of Vector Localized Waves Induced by the Fourth-Order Effect

Abstract

We investigate novel vector localized wave solutions in the coupled Lakshmanan-Porsezian-Daniel equa?tions, which describe the dynamics of the Heisenberg ferromagnetic spin chain. We present Tajiri-Watanabe breathers, rogue waves and resonant modes in both the degenerate and non-degenerate regions, together with the degenerate beating solitons. The fourth-order effect induces state transitions in both regions. In particular, the degenerate breathers can be transformed into solitons, whereas such transitions are absent in the coupled Hirota equations. Moreover, beating solitons can be converted into stable solitons only in the degenerate region, the phenomena not found in the Manakov system. We further uncover the state transitions of the resonant modes and derive the corresponding transition conditions for each branch. We derive the physical spectra and subsequently identify the state transition conditions in the spectral domain for both the degenerate and non-degenerate cases. These spectra provide an additional characterization of the transition dynamics. Finally, direct numerical simulations are performed to verify the validity of the exact solutions.