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