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

Pramana: Journal of physics

ASIT SAHA^3¹  TURGUT AK^1²  ABDUL HAMID KARA^4³  TUGBA AYDEMIR^2⁴ 

[1] Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo 737 136, India^3;Department of Transportation Engineering, Yalova University, 77100 Yalova, Turkey^1;School of Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa^4;Yalova University, 77100 Yalova, Turkey^2

关键词: Generalised Oskolkov equation;    shock wave;    unified method;    collocation;    quasiperiodicity;    chaos;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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. Consideringan 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 systemparameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

【 授权许可】

CC BY