Dissipative Periodic and Chaotic Patterns to the Kdv--Burgers and Gardner Equations

S.C. Mancas; Ronald Adams; Stefani Mancas

doi:10.1016/j.chaos.2019.07.006

Dissipative Periodic and Chaotic Patterns to the Kdv--Burgers and Gardner Equations

S.C. Mancas, Ronald Adams, Stefani Mancas

Embry-Riddle Aeronautical University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Chaos, Solitons Fractals
Volume	126
DOIs	https://doi.org/10.1016/j.chaos.2019.07.006
State	Published - Sep 2019

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Physical Sciences and Mathematics

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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{\textquoteright}nikov{\textquoteright}s theorem. ",

author = "S.C. Mancas and Ronald Adams and Stefani Mancas",

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language = "American English",

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AU - Adams, Ronald

AU - Mancas, Stefani

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PY - 2019/9

Y1 - 2019/9

N2 - 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.

AB - 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.

UR - https://www.sciencedirect.com/science/article/pii/S0960077919302589

U2 - 10.1016/j.chaos.2019.07.006

DO - 10.1016/j.chaos.2019.07.006

M3 - Article

SN - 1873-2887

VL - 126

JO - Chaos, Solitons Fractals

JF - Chaos, Solitons Fractals

ER -

Dissipative Periodic and Chaotic Patterns to the Kdv--Burgers and Gardner Equations

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