2025/11/28 by E. M. Gromov, Boris A. Malomed, Gromov, Evgeny M. +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2512.00189
openalex publication_date 2025/11/28 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
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.