Similarity representation of wave propagation in a nonlinear viscoelastic rod on a group theoretic basis
Similarity representation of wave propagation in a nonlinear viscoelastic rod, subjected to a velocity impact is constructed. By the use of a multiparameter dimensional group of transformations, under which the system of basic equations and auxiliary conditions are invariant, similarity transformations are obtained which are used to construct the similarity representation in the form of an ordinary nonlinear boundary value problem of the original system, consisting of a set of simultaneous nonlinear partial differential equations and the association boundary and initial conditions.
multiparameter dimensional group of transformations
ordinary nonlinear boundary value problem
set of simultaneous nonlinear partial differential equations
scientific article; zbMATH DE number 3980608
scientific article