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Article
Dissipative Periodic and Chaotic Patterns to the Kdv--Burgers and Gardner Equations
Chaos, Solitons & Fractals (2019)
  • S.C. Mancas, Embry-Riddle Aeronautical University
  • Ronald Adams
Abstract
We investigate the KdV-Burgers and Gardner equations with dissipation and external perturbation terms by the approach of dynamical systems. The stability of the equilibrium point is considered, and Hopf bifurcations are investigated after a certain scaling that reduces the parameter space of a three-mode dynamical system which now depends only on two parameters. In the case of the KdV-Burgers, we find homoclinic chaos by using Shil’nikov’s theorem. 
Publication Date
September, 2019
DOI
https://doi.org/10.1016/j.chaos.2019.07.006
Citation Information
S.C. Mancas and Ronald Adams. "Dissipative Periodic and Chaotic Patterns to the Kdv--Burgers and Gardner Equations" Chaos, Solitons & Fractals Vol. 126 (2019) p. 385 - 393
Available at: http://works.bepress.com/stefani_mancas/129/