Abstract
Two hyperbolic equations with a nonlinear coefficient multiplying the highest derivative are considered. The coefficient determines the velocity of nonlinear waves and characterizes the scattering properties of the medium. For stationary traveling-wave solutions, inverse problems are set up consisting of determining a nonlinear coefficient from the dependence of the period on the amplitude of the stationary oscillations. Nonlinear integral functional equations of the inverse problems are obtained and studied, and sufficient conditions for the existence and uniqueness of solutions to the inverse problems are steady-state. Evolution-type algorithms for solving functional equations are proposed. Solutions of test inverse problems are presented.
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Funding
This paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2019-1621.
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Translated by I. Ruzanova
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Baev, A.V. Solution of Inverse Problems for Wave Equation with a Nonlinear Coefficient. Comput. Math. and Math. Phys. 61, 1511–1520 (2021). https://doi.org/10.1134/S0965542521090049
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DOI: https://doi.org/10.1134/S0965542521090049