Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

M Przedborski, SC Anco - Journal of Mathematical Physics, 2017 - pubs.aip.org
A highly nonlinear, fourth-order wave equation that models the continuum theory of long
wavelength pulses in weakly compressed, homogeneous, discrete chains with a general
power-law contact interaction is studied. For this wave equation, all solitary wave solutions
and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The
solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude
in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear …
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