2001/07/12 by Xiaoyan Tang, Xiao-yan Tang, Sen-yue Lou +5
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0107027
13 pages, 8 figure
openalex publication_date 2001/07/12 · arxiv created 2001/09/18 · openalex created_date 2016/06/24 · arxiv updated 2019/08/17 · openalex updated_date 2026/07/28
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.