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.
Key words:wave equation, stationary solution, integral functional equation, blow-up mode.
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