(1+1)-dimensional turbulent and chaotic systems reduced from (2+1)-dimensional lax integrable dispersive long wave equation

After generalizing the Clarkson-Kruskal direct similarity reduction ansatz, one can obtain various new types of reduction equations. Especially, some lower-dimensional turbulent systems or chaotic systems may be obtained from the general form of the similarity reductions of a higher-dimensional Lax integrable model. Furthermore, an arbitrary three-order quasi-linear 'Equation, which includes the Korteweg de-Vnes Burgers equation and the general Lorenz equation as two special cases, has been obtained from the reductions of the (2+1)-dimensional dispersive long wave equation system. Some types of periodic and chaotic solutions of the system are also discussed.