Modeling the Evolution of Solitary Waves in the Engineering Materials

Abstract

To study the evolution of initial profile owing to weak nonlinearity of material, the propagation of longitudinal waves with the initial harmonic and bell-shaped profiles, transverse waves with initial profile in the form of Whittaker function, cylindrical waves with initial profile in the form of Macdonald function is analyzed theoretically and numerically. An comparative analysis is carried out for the solitary waves with different initial profiles basing on the obtained by authors solutions that includes an effect of the wave length (bottom), initial amplitude, and material parameters on the wave evolution.