Quasi-confined modes produced by the Lugiato-Lefever model with a localized pump and the pseudo-Raman term
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| Format: | Preprint |
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2025
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| _version_ | 1866911294021435392 |
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| author | Gromov, Evgeny M. Malomed, Boris A. |
| author_facet | Gromov, Evgeny M. Malomed, Boris A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-confined modes produced by the Lugiato-Lefever model with a localized pump and the pseudo-Raman term Gromov, Evgeny M. Malomed, Boris A. Pattern Formation and Solitons Optics 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. |
| title | Quasi-confined modes produced by the Lugiato-Lefever model with a localized pump and the pseudo-Raman term |
| topic | Pattern Formation and Solitons Optics |
| url | https://arxiv.org/abs/2512.00189 |