  An analysis of nonlinear transverse shear wave has been carried out on
non-Newtonian viscoelastic liquid using generalized hydrodynamic(GH) model. The
nonlinear viscoelastic behavior is introduced through velocity shear dependence
of viscosity coefficient by well known Carreau -Bird model. The dynamical
feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam (FPU)
problem. Numerical solution has been obtained which shows that initial periodic
solutions reoccur after passing through several patterns of periodic waves. A
possible explanation for this periodic solution is given by constructing
modified Korteweg de Vries (mKdV) equation. This model has application from
laboratory to astrophysical plasmas as well as biological systems.

Plasma Physics