  After extending the Clarkson-Kruskal's direct similarity reduction ansatz to
a more general form, one may obtain various new types of reduction equations.
Especially, some lower dimensional turbulence systems or chaotic systems may be
obtained from the general type of similarity reductions of a higher dimensional
Lax integrable model. Especially, the Kuramoto-Sivashinsky equation and an
arbitrary three order quasilinear equation which includes the Korteweg de-Vries
Burgers equation and the general Lorenz equation as two special cases are
obtained from the reductions of the (2+1)-dimensional dispersive long wave
equation system. Some types of periodic and chaotic solutions of the
(2+1)-dimensional dispersive long wave equation system are also discussed.
