Order to chaos transitions in damped KdV equation modeled as a jerk equation

Subha Samanta, Pankaj Kumar Shaw, M. S. Janaki, A. N.Sekar Iyengar

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The possibility of finding chaos in a KdV like system in the absence of any external forcing is explored without reducing its order by treating it as a third order Jerk equation. While bounded solutions with periodic nature exist for both right and left traveling wave solutions of the KdV equation, inclusion of terms that signify damping lead to chaotic behavior only for left moving waves. The bifurcation diagram obtained for suitable choice of the parameters shows interesting phenomena such as Hopf and period doubling bifurcations. To characterize the chaotic behavior, the spectrum of Lyapunov exponent is studied. Domains of stable and unstable solutions with the boundaries marking transitions have been identified in the parameter space.

Original languageEnglish
Article number045602
JournalPhysica Scripta
Volume94
Issue number4
DOIs
StatePublished - 31 Jan 2019
Externally publishedYes

Keywords

  • KdV-Burgers equation
  • chaos
  • solitary wave

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy (all)

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