Quasi-confined modes produced by the Lugiato-Lefever model with a localized pump and the pseudo-Raman term

Abstract

We introduce an extended nonlinear Lugiato-Lefever equation (LLE) with the pseudo-stimulated-Raman-scattering (pseudo-SRS) cubic term, linear damping/gain, and spatial inhomogeneous (weakly or strongly localized) pump. The LLE is derived, in the extended adiabatic approximation, from the underlying Zakharov system (ZS), which includes a viscosity term, acting on its low-frequency (LF) component, and the pump supporting the high-frequency (HF) one. Dynamics of quasi-solitons in the model is addressed by means of analytical and numerical methods. The sech-based approximation for the quasi-soliton predicts it as a stable fixed point (FP) of the system of evolution equations for the moments of the system moments (the HF norm, wave momentum, and center-of-mass coordinate). The attraction basin of the FP is identified too. The prediction is corroborated by direct simulations of the full LLE. A quasi-singular mode, supported by the delta-functional pump, is briefly considered too.