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(1+1)-Dimensional Turbulent and Chaotic Systems Reduced from
(2+1)-Dimensional Lax Integrable Dispersive Long Wave Equation
TANG Xiao-Yan,, LOU Sen-Yue,,, and
ZHANG Ying
Communications in Theoretical Physics
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.
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