• A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas–Lenells model

• Fulltext

https://www.ias.ac.in/article/fulltext/pram/095/0041

• Keywords

Perturbed Fokas–Lenells model; $(G'/G^2)$-expansion method; bifurcation analysis.

• Abstract

In this paper, a diverse range of travelling wave structures of perturbed Fokas–Lenells model (p-FLM) is obtained by using the extended $(G'/G^2)$-expansion technique. The existence of the obtained solutions is guaranteed by reporting constraint conditions. Then, the governing model is converted into the planer dynamical system with the help of Gallelian transformation. Every possible form of phase portraits is plotted for pertinent parameters, viz. $k$, $\beta$, $d_1$, $d_2$, $d_3$. We also used the Runge–Kutta fourth-order technique to extract the nonlinear periodic solutions of the considered problem and outcomes are presented graphically. Furthermore, quasiperiodic and chaotic behaviour of p-FLM is analysed for different values of parameters after deploying an external periodic force. Quasiperiodic–chaotic nature is observed for selected values of parameters $k$, $\beta$, $d_1$, $d_2$, $d_3$ by keeping the force and frequency of the perturbed dynamical system fixed. The sensitive analysis is employed on some initial value problems (IVPs). It is seen that de-sensitisation is present in the perturbed dynamical system while for the same values of parameters, the unperturbed dynamical system has a nonlinear periodic solution.

• Author Affiliations

1. Department of Mathematics, Namal Institute, 30 KM Talagang Road, Mianwali 42250, Pakistan
2. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran
3. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
4. Mathematics Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt

• Pramana – Journal of Physics

Volume 95, 2021
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Posted on July 25, 2019