Existence of chaos in weakly quasilinear systems

Pages: 1331 - 1344, Volume 10, Issue 5, September 2011

doi:10.3934/cpaa.2011.10.1331       Abstract        References        Full Text (357.8K)       Related Articles

Y. Charles Li - Department of Mathematics, University of Missouri, Columbia, MO 65203, United States (email)

Abstract: The aim of this article is twofold: (1). develop a strategy to prove the existence of chaos in weakly quasilinear systems, (2). strengthen the existing results on chaos in partial differential equations. First, we study a sine-Gordon equation containing weakly quasilinear terms, and existence of chaos is proved. Then, we study a Ginzburg-Landau equation containing weakly quasilinear terms, and existence of chaos is proved under generic conditions. Finally, in the Appendix, we prove the existence of chaos in a reaction-diffusion equation.

Keywords:  Quasilinear system, chaos, homoclinic orbit, sine-Gordon equation, Ginzburg-Landau equation.
Mathematics Subject Classification:  Primary 35, 37; Secondary 34, 46.

Received: February 2009;      Revised: August 2010;      Published: April 2011.

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