Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Traveling waves in compressible elastic rods

Pages: 151 - 167, Volume 6, Issue 1, January 2006      doi:10.3934/dcdsb.2006.6.151

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Jonatan Lenells - Department of Mathematics, Lund University, PO Box 118, 22100 Lund, Sweden (email)

Abstract: We determine all weak traveling wave solutions of a model for nonlinear dispersive waves in cylindrical compressible hyperelastic rods. Besides the previously known smooth, peaked, and cusped solutions, the equation is shown to admit compactons, stumpons, and fractal-like waves.

Keywords:  Elasticity, Traveling waves, Nonlinear wave equations.
Mathematics Subject Classification:  Primary: 37N15, 74B20, 35Q72.

Received: August 2004;      Revised: September 2005;      Available Online: October 2005.