Non-degenerate rogue waves and multiple transitions in systems of three-wave resonant interaction

Abstract

Non-degenerate rogue waves (RWs) and multiple transitions between RWs and solitons arising from vector three-wave resonant interaction are studied analytically and numerically. In contrast to the conventional degenerate RWs, such non-degenerate RWs consist of two fundamental RWs each with individual Lax spectral parameter. We show distinctive continuous transitions from bright (dark) RWs to four-petal RWs to dark (bright) solitons as the relative frequency between the wave components increases. The underlying mechanism of such processes is the non-monotonic variation of the energy exchanges between different components of the waves. We further reveal the transition dynamics of non-degenerate RWs. Finally, we confirm numerically the robustness of the transition dynamics in the presence of spontaneous modulation instability induced by white noise. Our results provide insights into the RW formation and the multiple transitions in systems with three-wave resonant interaction, and may offer the possibility of experimental observations in multi-component resonant processes.