  We investigate spatio-temporal structures in sheared polymer systems by
solving a time-dependent Ginzburg-Landau model in two dimensions. (i) In
polymer solutions above the coexistence curve, crossover from linear to
nonlinear regimes occurs with increasing the shear rate. In the nonlinear
regime the solution behaves chaotically with large-amplitude composition
fluctuations. A characteristic heterogeneity length is calculated in the
nonlinear regime. (ii) We also study dynamics of shear-band structures in
wormlike micellar solutions under the condition of fixed stress. The average
shear rate exhibits large temporal fluctuations with occurrence of large
disturbances in the spatial structures.
