Performance of a hybrid computational scheme on traveling waves and its dynamic transition for Gilson–Pickering equation

Turgut Ak, Asit Saha () and Sharanjeet Dhawan ()
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Turgut Ak: Armutlu Vocational School, Yalova University, Armutlu, 77500 Yalova, Turkey
Asit Saha: Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, East-Sikkim 737136, India
Sharanjeet Dhawan: Department of Mathematics, Central University of Haryana, 123029 Haryana, India

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 04, 1-17

Abstract: In this work, we developed a hybrid scheme for Gilson–Pickering equation by extracting advantageous features of collocation method and B-splines. Collocation method involves satisfying a differential equation to some tolerance at finite number of points and has low computational cost. The idea is to extract the superior accuracy and smoothness of B-spline functions with the low computational cost of collocation scheme. In the vision of a superficial periodic force, we obtain the quasiperiodic and chaotic behaviors of the forced Gilson–Pickering equation by perusing phase portrait technique, time series and Poincaré section. The sequel of frequency (ω) of the superficial periodic force is very prime in case of transition from weakly chaotic feature to quasiperiodic feature of the forced Gilson–Pickering equation.

Keywords: Gilson–Pickering equation; finite element method; collocation; solitary wave; chaotic behavior (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0129183119500281

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