We investigate the longitudinal dynamics of multisection semiconductor lasers based on a model, where a hyperbolic system of partial differential equations is nonlinearly coupled with a system of ordinary differential equations. We present analytic results for that system: global existence and uniqueness of the initial‐boundary value problem, and existence of attracting invariant manifolds of low dimension. The flow on these manifolds is approximately described by the so‐called mode approximations which are systems of ordinary differential equations. Finally, we present a detailed numerical bifurcation analysis of the two‐mode approximation system and compare it with the simulated dynamics of the full PDE model.
Santrauka. Mes nagrinėjame išilginę daugiasekcijinių puslaidininkinių lazerių dinamiką, kuri yra nusakoma netiesiškai susietomis hiperboline diferencialinių lygčių dalinėmis išvestinėmis bei paprastųjų diferencialinių lygčių sistemomis. Mes pateikiame sekančias šios sistemos savybes: globalaus pradinio‐kraštinio uždavinio sprendinio egzistavimas bei vienatis; mažos dimensijos pritraukiančiojo invariantinio hiperpaviršiaus egzistavimas. Modelio dinamika šiame hiperpaviršiuje yra apytiksliai nusakoma paprastųjų diferencialinių lygčių sistema. Pabaigoje mes pateikiame detalią skaitinę šios paprastųjų diferencialinių lygčių sistemos bifurkacinę analizę ir lyginame ja su skaitiškai nustatyta pilnos diferencialinių lygčių dalinėmis išvestinėmis sistemos dinamika.
Sieber, J., Radžiūnas, M., & Schneider, K. R. (2004). Dynamics of multisection semiconductor lasers. Mathematical Modelling and Analysis, 9(1), 51-66. https://doi.org/10.3846/13926292.2004.9637241
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