Abstract
The article studies the nonlinear longitudinal oscillations of an elastic rod in the presence of a non-stationary external source described by a nonlinear differential equation that admits the widest group of Lie transformations among the equations of the main model that describes this physical process. The model under study describes longitudinal oscillations at the presence of a very strong external influence, singular at the initial moment of time. We studied invariant submodels of this model which are described by exact solutions. We found their physical meaning. For some specific values of the parameters that determine these submodels the graphs of the distribution of the longitudinal displacement are constructed.
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