Abstract
Explanations of the term “strongly nonlinear wave” are given, and a possible classification of the corresponding mathematical models is described. The parameters are discussed for which it is reasonable to call the mechanical and electromagnetic waves “strong” and distinguish them from weakly nonlinear waves, the nonlinear effects in which can also be strongly expressed. Exact “stationary” solutions with singularities are studied in the example of evolution equations with quadratic and modular nonlinearities. It is shown that these solutions in fact are not stationary, since the singularities arising in them are rapidly destroyed due to the manifestation of nonlinear and dissipative properties of the medium.
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