Abstract
Using the group analysis methods, for the Ovsyannikov equation with maximal symmetry which describes steady-state oscillations in a continuous inhomogeneous medium, we obtain exact solutions to boundary-value problems for some regions (generalized Poisson formulas), which in particular can serve as test solutions for simulating steady-state oscillations in continuous inhomogeneous media. We find operators acting on the set of solutions in a one-parameter family of these equations.
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