Existence of chaos in weakly quasilinear systems | Zendy

Y. Charles Li | Zendy

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Existence of chaos in weakly quasilinear systems

Author(s) -

Y. Charles Li

Publication year - 2011

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2011.10.1331

Subject(s) - chaos (operating system) , mathematics , partial differential equation , sine , sine gordon equation , differential equation , mathematical analysis , physics , mathematical physics , computer science , nonlinear system , quantum mechanics , soliton , geometry , computer security

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.

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