Strongly nonlinear waves

Abstract

This short chapter deals with modulated waves described by strongly nonlinear Klein-Gordon equation. Mechanical equivalent for this model can be represented by the infinite linear string on elastic foundation. In this case, the principal (carrying) wave can be approximated by polynomials or other elementary functions of the triangular sine wave based on the algorithms of the previous chapter. Then the differential equations for slow varying modulating components are derived by using the Whitham assumptions and the specific boundary conditions associated with nonsmooth argument substitutions.