NONLINEAR SCHRÖDINGER EQUATIONS WITH DELAY: EXACT SOLUTIONS, REDUCTIONS, AND TRANSFORMATIONS
https://doi.org/10.26583/vestnik.2024.5.6
EDN: PALOUN
Abstract
Schrödinger equations with cubic and more complex nonlinearities containing the desired function with a delayed argument are considered. The physical considerations that can lead to the appearance of a delay in such nonlinear equations and models are expressed. One-dimensional reductions are described that lead the studied partial differential equations with delay to simpler ordinary differential equations or ordinary differential equations with delay. Exact solutions of the nonlinear Schrödinger equation of general form with delay, which are expressed in quadratures, are found. Special attention is paid to three equations with cubic nonlinearity, which allow simple solutions in elementary functions, as well as more complex exact solutions with generalized separation of variables. In addition to nonlinear Schrödinger equations with constant delay, some more complex equations with variable delay of general form are also studied. The results obtained can be useful for testing mathematical models described by the nonlinear Schrödinger equation with delay.
Keywords
nonlinear Schrödinger equation with delay,
partial differential equations with delay,
exact solutions,
solutions in quadratures,
generalized separable solutions
Supporting agencies: The work was carried out on the topics of the state assignment (state registration no. 124012500440-9 and FSWU-2023-0031).
About the Authors
A. D. Polyanin
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
Russian Federation
Russian Federation
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
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Review
For citations:
Polyanin A.D., Kudryashov N.A. NONLINEAR SCHRÖDINGER EQUATIONS WITH DELAY: EXACT SOLUTIONS, REDUCTIONS, AND TRANSFORMATIONS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2024;13(5):340-349. (In Russ.) https://doi.org/10.26583/vestnik.2024.5.6. EDN: PALOUN
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