A.S. Zakharov1, A.M. Savchuk2, V.V. Morozov3, D.A. Zvonarev4

1 Lomonosov Moscow State University (Moscow, Russia)
2 Yaroslavl State Agricultural Academy (Yaroslavl, Russia)
3 Tula State University (Tula, Russia)
1 zakharov.as17@physics.msu.ru, 2 savchuk@cosmos.msu.ru, 4zvonarev@cz71.ru

The article presents a description of the superresolution mode in space monitoring radars and the minimization of the non-identity of the amplitude distribution necessary for its implementation. The destabilizing factor in the case of non-identity is thermal processes and nonequilibrium losses in transmission channels that change the amplitude of the signal.

Due to the fact that a dynamic temperature change in space and time occurs in the sublattice of the active phased array antenna array, it is proposed to formalize a model for calculating corrections to the amplitude of signals, taking into account the known amplitude distribution calibration algorithm. At the same time, in order to formalize nonequilibrium processes in transmission channels, it is proposed to use the modified nonlinear Schrodinger equation and combine it with the calculation of thermal processes.

It is shown that the obtained nonlinear Schrodinger equation can be solved by solving the Zakharov-Shabat problem for the perturbed case, which makes it possible to solve this equation operationally.

Based on real data on changes in the amplitude of the signal under the influence of thermal processes, an initial boundary value problem of thermal conductivity in the sublattice of an active phased array antenna is obtained to find changes in the amplitude of the signal. An approximation of data on phase and amplitude changes for thermostatically controlled receiving and transmitting modules is presented, according to which the original exponential dependences of signal amplitudes on the steady-state temperature are obtained.

An important advantage of the proposed model is the joint consideration of deterministic thermal processes and nonequilibrium processes in transmission channels by solving two different initial boundary value problems, thereby solving both theoretical and practical problems.

Zakharov A.S., Savchuk A.M., Morozov V.V., Zvonarev D.A. Nonlinear Schrodinger equation in a model for estimating and compensating the influence of thermal processes on the ampli-tude-phase distribution. Nonlinear World. 2024. V. 22. № 4.
P. 129–136. DOI: https://doi.org/10.18127/ j20700970-202404-17 (In Russian)

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