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October 12, 2026
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Quasi-confined modes produced by the Lugiato-Lefever model with a localized pump and the pseudo-Raman term

Physics Letters A. 2026. Vol. 567. Article 131219.
Gromov E., Malomed B. A.

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 (weekly or strongly localized) pump. The LLE is derived, in the extended adiabatic approximation, from the underlying Zakharov’s 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 system’s moments (the HF norm, wave momentum, and center-of-mass coordinate). The FP’s attraction basin 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.

Research target: Physics Mathematics
Language: English
Full text
DOI
Keywords: солитоннеподвижная точкаfixed pointsolitonsнелинейное уравнение ШредингераStimulated Raman scatteringNonlinear Schrödinger EquationsExtended Lugiato-Lefever EquationZakharov’s SystemРасширенное уравнение Лугиато-ЛефевраСистема ЗахароваВынужденное комбинационное рассеяние
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