Browsing by Author "Jhangeer, Adil"

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Citation Count: Jhangeer, Adil;...et.al. (2020). "Construction of traveling waves patterns of (1+n)-dimensional modified Zakharov-Kuznetsov equation in plasma physics", Results in Physics, Vol.19.
Construction of traveling waves patterns of (1+n)-dimensional modified Zakharov-Kuznetsov equation in plasma physics
(2020) Jhangeer, Adil; Munawar, Maham; Riaz, Muhammad Bilal; Baleanu, Dumitru; 56389
In this research, we examine the modified model of (1+n)-dimensional Zakharov-Kuznetsov (ZK) equation, which will be used to analyze the nature of weakly nonlinear traveling waves in the existence of a constant magnetic area in a plasma comprising in cold ions and hot isothermal electrons. The modified Zakharov-Kuznetsov (mZK) equation will have solutions describing the traveling solitary waves, using the extended [Formula Presented]-expansion method and extended direct algebraic method gives way to the mZK equation regulating the transmission of ion dynamics for nonlinear traveling waves in a plasma. The sufficient conditions for the stability and existence of the traveling wave solutions are reported. Semi-dark, rational, and singular solitary wave solutions are computed. Graphical interpretations of certain practical solutions for specific values of parameters have also been available. The research findings reported throughout this evaluation are fresh and from which this model is employed to analyze waves in numerous plasmas, could be valuable and important. Subsequently, there are concluding remarks mentioned.
Citation Count: Riaz, Muhammad Bilal;...et.al. (2022).
Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative
(2022) Riaz, Muhammad Bilal; Jhangeer, Adil; Awrejcewicz, Jan; Baleanu, Dumitru; Tahir, Sana; 56389
This study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa–Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of beta derivative and truncated M-fractional derivative. We employ a new direct algebraic technique for the nonlinear Sasa–Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of the considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three-dimensional graphs. This shows that for lower fractional orders, i.e., b ¼ 0:1, the magnitude of truncated M-fractional derivative is greater whereas for increasing fractional orders, i.e., b ¼ 0:7 and b ¼ 0:99, the magnitude remains the same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.
Citation Count: Jarad, Fahd;...et.al. (2022). "Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method", Results in Physics, Vol.37.
Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method
(2022) Jarad; Jhangeer, Adil; Awrejcewicz, Jan; Riaz, Muhammad Bilal; Junaid-U, Rehman M.; 234808
This work is focused to analyze the generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) by the Lie symmetry method. GCBS equation has been utilized to explain the wave profiles in soliton theory. GCBSE was constructed by Bogoyavlenskii and Schiff in different ways (explained in the introduction section). With the aid of Lie symmetry analysis, we have computed the symmetry generators of the GCBSE and commutation relation. We observed from the commutator table, translational symmetries make an Abelian algebra. Then by using the theory of Lie, we have discovered the similarity variables, which are used to convert the supposed nonlinear partial differential equation (NLPDE) into a nonlinear ordinary differential equation (NLODE). Using the new auxiliary method (NAM), we have to discover some new wave profiles of GCBSE in the type of few trigonometric functions. These exits some parameters which we give to some suitable values to attain the different diagrams of some obtained solutions. Further, the GCBSE is presented by non-linear self-adjointness, and conserved vectors are discovered corresponding to each generator.
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: Riaz, Muhammad Bilal...et al. (2021). "Nonlinear self-adjointness, conserved vectors, and traveling wave structures for the kinetics of phase separation dependent on ternary alloys in iron (Fe-Cr-Y (Y = Mo, Cu))", RESULTS IN PHYSICS, Vol. 25.
Nonlinear self-adjointness, conserved vectors, and traveling wave structures for the kinetics of phase separation dependent on ternary alloys in iron (Fe-Cr-Y (Y = Mo, Cu))
(2021) Riaz, Muhammad Bilal; Baleanu, Dumitru; Jhangeer, Adil; Abbas, Naseem; 56389
The present exploration is concerned with fundamental elements corresponding to the phase decomposition in (Fe-Cr-Mo) and (Fe-Cr-Cu) ternary composites. For the ternary composites of iron, we examine the dynamical behavior of the phase separation. The dynamic of this separation is depicted by a model known as the CahnHilliard equation. The nonlinear self-adjointness for the model under consideration is taken into account. The conserved quantities are calculated with the help of the direct method. For each symmetry generator, we have reduced the considered equation into non-linear ordinary differential equations (ODEs). Also, we have computed the optimal system of the equation under study to find the similarity reduction. Also, the traveling wave structures of the Cahn-Hilliard equation are obtained with the modified simple equation (MSE) technique. Moreover, solitary wave structures is exhibited graphically in the form of 3D, 2D and contour plots.
Citation Count: Asjad, Muhammad Imran;...et.al. (2022). "Nonlinear wave train in an inhomogeneous medium with the fractional theory in a plane self-focusing", AIMS Mathematics, Vol.7, No.5, pp.8290-8313.
Nonlinear wave train in an inhomogeneous medium with the fractional theory in a plane self-focusing
(2022) Asjad, Muhammad Imran; Faridi, Waqas Ali; Jhangeer, Adil; Aleem, Maryam; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; 56389
The aim of study is to investigate the Hirota equation which has a significant role in applied sciences, like maritime, coastal engineering, ocean, and the main source of the environmental action due to energy transportation on floating anatomical structures. The classical Hirota model has transformed into a fractional Hirota governing equation by using the space-time fractional Riemann-Liouville, time fractional Atangana-Baleanu and space-time fractional β differential operators. The most generalized new extended direct algebraic technique is applied to obtain the solitonic patterns. The utilized scheme provided a generalized class of analytical solutions, which is presented by the trigonometric, rational, exponential and hyperbolic functions. The analytical solutions which cover almost all types of soliton are obtained with Riemann-Liouville, Atangana-Baleanu and β fractional operator. The influence of the fractional-order parameter on the acquired solitary wave solutions is graphically studied. The two and three-dimensional graphical comparison between Riemann-Liouville, Atangana-Baleanu and β-fractional derivatives for the solutions of the Hirota equation is displayed by considering suitable involved parametric values with the aid of Mathematica.
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.