Time-independent harmonics dispersion relation for time-evolving nonlinear waves.

ABSTRACT: We present a theory for the dispersion of generated harmonics in a traveling nonlinear wave. The harmonics dispersion relation (HDR), derived by the theory, provides direct and exact prediction of the collective harmonics spectrum in the frequency–wave number domain and does so without prior knowledge of the u = u(x, t) solution. It is valid throughout the evolution of a distorting unbalanced wave or the steady-steady propagation of a balanced wave with waveform invariance. The new relation is shown to be a special case of the general nonlinear dispersion relation (NDR), which is also derived. The theory is examined on a diverse range of cases of one-dimensional elastic waves and shown to hold irrespective of the spatial form of the initial wave profile, type an

SUBMITTER: Khajehtourian R 

PROVIDER: S-EPMC8654300 | biostudies-literature | 2021 Dec

REPOSITORIES: biostudies-literature