Nonlinear modulation of longitudinal waves in a kelvin-voigt solid

In this paper nonlinear modulation of one dimensional longitudinal waves in a Kelvin-Voigt solid is considered. The constituent material is assumed to be homogenous, isotropic and finite linear viscoelastic. Under these assumptions, the equation of motion governing the propagation of nonlinear longitudinal waves in this viscoelastic medium is given. Then this equation is examined asymptotically for wave modulation by employing a perturbation method namely the method of multiple scales. Then, in the analysis under the balance between weak nonlin-earity and linear dispersion and counterbalance between linear parabolic loss (gain) for dispersion and cubic nonlinear gain (loss), it is shown that the nonlinear modulation of longitudinal waves is characterized by a complex Ginzburg-Landau (CGL) equation. The dissipative bright soliton solution of the CGL equation is constructed. The effect of linear and nonlinear material properties of the viscoelastic media to the structure of dissipative bright soliton solution is examined by choosing different artificial material models.