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Pramana

, 90:78 | Cite as

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

  • Turgut Ak
  • Tugba Aydemir
  • Asit Saha
  • Abdul Hamid Kara
Article

Abstract

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Keywords

Generalised Oskolkov equation shock wave unified method collocation quasiperiodicity chaos 

PACS NOs

12.60.Jv 12.10.Dm 98.80.Cq 11.30.Hv 

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  • Turgut Ak
    • 1
  • Tugba Aydemir
    • 2
  • Asit Saha
    • 3
  • Abdul Hamid Kara
    • 4
  1. 1.Department of Transportation EngineeringYalova UniversityYalovaTurkey
  2. 2.Yalova UniversityYalovaTurkey
  3. 3.Department of MathematicsSikkim Manipal Institute of Technology, Sikkim Manipal UniversityMajitar, RangpoIndia
  4. 4.School of MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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