Modulational Instability, Vector Solitons and Extreme Amplitude Envelopes in Asymmetric Coupled Nonlinear Schrödinger Equations

An interesting aspect of wave propagation in nonlinear dispersive media is the emergence of localized structures such as solitons, solitary waves, breathers and rogue waves (freak waves). Analytical models for wavepacket propagation can be reduced through perturbative approaches into a (or more) nonlinear Schrödinger (NLS) equation(s) describing the dynamics of a modulated wavepacket envelope. In a generic manner, the dynamics of two co-propagating (and interacting) wavepackets with different carrier wavenumber and frequency is described by a pair of coupled NLS (CNLS) equations, whose coefficients do not present any particular symmetry. In this short paper, we investigate such a(n asymmetric) CNLS system, expressed in a generalized form, considering a nearly-symmetric configuration as a case study (i.e. close to -but not indentical to- the well known Manakov model). The system’s modulational instability (MI) profile is analyzed in terms of the group velocity misfit (difference) and also (independently) in terms of the mismatch of a nonlinear coupling coefficient. Extreme amplitude (rogue-wave like) envelopes are shown to exist, as components of bright-dark or bright-bright vector soliton configurations.