Browsing by Author "Junaid-U-Rehman, M."

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Citation Count: Jhangeer, Adil...et al. (2020). "Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii–Kadomtsev–Petviashvili equation", Results in Physics, Vol. 19.
Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii–Kadomtsev–Petviashvili equation
(2020) Jhangeer, Adil; Hussain, Amjad; Junaid-U-Rehman, M.; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this paper, the Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation is taken into consideration by means of Lie symmetry analysis. Infinitesimal generators are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Henceforth, conjugacy classes of abelian algebra are used to find the similarity reductions, which convert the considered equation into ordinary differential equations (ODEs). Further, these ODEs are taken into consideration, and travelling wave structures are computed by applying different techniques. Moreover, the discussed model is discussed by means of nonlinear selfadjointness and conservation laws are derived for each Lie symmetry generator. For specific values of the physical parameters of the equation under discussion, the graphical behaviour of some solutions is depicted. © 2020 The Authors
Citation Count: Jhangeer, Adil...et al. (2021). "Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation", Chaos, Solitons and Fractals, Vol. 143.
Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation
(2021) Jhangeer, Adil; Hussain, Amjad; Junaid-U-Rehman, M.; Baleanu, Dumitru; Riaz, Muhammad Bilal; 56389
In this paper, the nonlinear modified Gardner (mG) equation is under consideration which represents the super nonlinear proliferation of the ion-acoustic waves and quantum electron-positronion magneto plasmas. The considered model is investigated with the help of Lie group analysis. Lie point symmetries are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Furthermore, the one-dimensional optimal system of subalgebras is developed by adjoint technique and then we compute the similarity reductions corresponding to each vector field present in the optimal system, with the help of similarity reduction method we have to convert the PDE into the ODE. Some exact explicit solutions of obtained ordinary differential equations were constructed by the power series technique. With the aid of the Galilean transformation, the model is transformed into a planer dynamical system and the bifurcation behaviour is recorded. All practicable types of phase portraits with regard to the parameters of the problem considered are plotted. Meantime, sensitivity is observed by utilizing sensitivity analysis. In addition, the influence of physical parameters is studied by the application of an extrinsic periodic power. With additional perturbed term, quasi-periodic and quasi-periodic-chaotic behaviours is reported.