(1+1)-Dimensional Turbulent and Chaotic Systems Reduced from (2+1)-Dimensional Lax Integrable Dispersive Long Wave Equation**The project supported by the Nati nal Outstanding Youth Foundation of China, the Research Fund for Doctoral Program of Higher Education of China, and the Natural Science Foundation of Zhejia ng Province of China

Abstract

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-Vries 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.