Browsing by Author "Butt A.R."

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A new exploration of some explicit soliton solutions of q-deformed Sinh-Gordon equation utilizing two novel techniques
(2023-03-01) Raza N.; Butt A.R.; Arshed S.; Kaplan M.
In the present work, the q-deformed Sinh-Gordon equation considered by performing new extended generalized Kudryashov method and improved tan(Φ2)-expansion method. Thanks to these methods, we can effectively obtain rational, hyperbolic and trigonometric solutions by specially choosing the parameters for the existence of solutions. The proposed equation expands the possibilities for modeling physical systems in which symmetry is broken. The obtained solutions are graphically illustrated.
An effective computational approach and sensitivity analysis to pseudo-parabolic-type equations
(2021-01-01) Kaplan M.; Butt A.R.; Thabet H.; Akbulut A.; Raza N.; Kumar D.
The researchers have developed numerous analytical and numerical techniques for solving fractional partial differential equations most of which provide approximate solutions. Exact solutions, however, are vitally important in a convenient conception of the qualitative properties of the concerned phenomena and processes. In this paper, the pseudo-parabolic-type equations with conformable fractional derivatives are reduced to conformable fractional nonlinear ordinary differential equations by implementing a simple wave transformation. An important benefit of the proposed transformation is that it yields analytical solutions of the conformable pseudo-parabolic type equations by applying the exponential rational function strategy. The sensitivity behaviour of the model has been mentioned thoroughly.
An exploration of novel soliton solutions for propagation of pulses in an optical fiber
(2022-07-01) Raza N.; Arshed S.; Kaplan M.; Butt A.R.
In this article, the propagation of pulses in optical fiber has been studied by considering the nonlinear partial differential equation (NPDE). The proposed model is investigated using two analytical techniques namely the Sine-Gordon expansion (SGE) procedure and the modified auxiliary equation (MAE) method. The trigonometric function, hyperbolic function, and rational function solutions have been extracted from the proposed methods. The employed procedures are compatible in obtaining traveling wave solutions. Moreover, the obtained results are assisted with 3D graphs to demonstrate the physical significance and dynamical behaviors by using different parameter values.
Symbolic computation and sensitivity analysis of nonlinear Kudryashov's dynamical equation with applications
(2021-10-01) Raza N.; Seadawy A.R.; Kaplan M.; Butt A.R.
This article aims to identify solitary wave solutions to a nonlinear Kudryashov's equation utilizing an exponential rational function method and Painlevé approach. This model is used to interpret the propagation of modulated envelope signals which disseminate with some group velocity. These two different methods are applied to build analytical solutions of the model that are relatively new and effective to solve the nonlinear evolution equation. Hyperbolic wave function and kink solitons are two types of traveling wave solutions that can be obtained using these techniques. For the existence of these solitons, constraint conditions on the parameters have also been listed. Graphical illustrations have also been given to understand the physical significance of the proposed model. In the end stability analysis of the obtained solution is carried out for depicting the importance of the model.