Ghost Interaction of Breathers

Abstract

Mutual interaction of localized nonlinear waves, e.g., solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. Here we report the observation of a novel type of breather interaction in telecommunication optical fibers, in which two identical breathers propagate with opposite group velocities. Under controlled conditions, neither amplification nor annihilation occurs at the collision point and most interestingly, the respective envelope amplitude, resulting from the interaction, almost equals another envelope maximum of either oscillating and counterpropagating breather. This ghost-like breather interaction dynamics is fully described by an N-breather solution of the nonlinear Schrödinger equation.

Observation of modulation instability and rogue breathers on stationary periodic waves

“…Introduction. During the last decades, the modulation instability (MI) phenomenon have attracted a significant research interest in a variety of nearly-conservative wave systems described by the nonlinear Schrödinger equation (NLSE) in its many forms [1][2][3][4][5][6][7][8]. This includes the linear stability analysis of the plane wave solution and the subsequent nonlinear stage of MI, namely the formation of localized waves such as solitons and breathers, as well as multi-breather complexes.…”

Vector breathers in the Manakov system

“…Meanwhile, experimental observation of various aspects of the integrable scalar NLSE dynamics and statistics has been successfully performed in many different works, see, for example, Refs. 14, 17–24, 78, 79. In addition, the development of vector MI and vector dark rogue waves has been studied experimentally in a Manakov fiber system 40,80 .…”

“…The scalar NLSE breathers have been the focus of the studies for the past decades, revealing such fundamental building blocs of the breather dynamics as Kuznetsov, Akhmediev, Peregrine, and Tajiri‐Watanabe solutions; 5,11–13 as well as superregular and ghost interaction patterns, 14–17 and breather wave molecules 17 . All these scenarios of nonlinear wavefield evolution have been confirmed experimentally with optical, hydrodynamical, and plasma setups 14,17–24 . In addition, the breathers play an essential role in the formation of rational rogue waves, 25,26 modulation instability (MI) development, 11,27 and in the dynamics and statistics of complex nonlinear random wave states 28–31 …”

“…17 All these scenarios of nonlinear wavefield evolution have been confirmed experimentally with optical, hydrodynamical, and plasma setups. 14,[17][18][19][20][21][22][23][24] In addition, the breathers play an essential role in the formation of rational rogue waves, 25,26 modulation instability (MI) development, 11,27 and in the dynamics and statistics of complex nonlinear random wave states. [28][29][30][31] In this work, we consider the vector two-component extension of the NLSE-the Manakov system.…”

Nonlinear interactions of two-kink-breather solution in Yu-Toda-Sasa-Fukuyama equation by modulated phase shift

“…These above examples of resonant interactions were studied in the case where the phase shift is singular, and it is pleasing to note that Tajiri et al considered the interactions of periodic solitons in the case where the phase shift is non-singular, i.e., repulsive and attractive interactions [36,37]. Such attractive or repulsive interactions have been observed in many experiments, so it is important to study the effects of phase shift on nonlinear wave interactions [38,39]. In 2011, the attractive and repulsive interactions of the quasi-line soliton of the KP equation are studied by Tajiri et al [40].…”