Consideration in this paper is the Cauchy problem of a generalized hyperelastic-rod wave equation. We first derive a wave-breaking mechanism for strong solutions, which occurs in finite time for certain initial profiles. In addition, we determine the existence of some new peaked solitary wave solutions.
"Wave-Breaking Phenomena and Existence of Peakons for a Generalized Compressible Elastic-Rod Equation." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/876849