Dispersive–dissipative solitons in nonlinear solids

Abstract

It is found that the propagation of long nonlinear longitudinal strain waves in an elastic rod embedded in a viscoelastic external medium may be governed by a nonlinear dispersive–dissipative equation with an appropriate input–output energy balance. This equation admits exact traveling solitary wave solutions. When dissipation is small enough an initially dissipationless strain solitary wave is shown to transform to a dissipative solitary wave with prescribed parameters.