MUHAMMAD ASAD IQBAL
Articles written in Pramana – Journal of Physics
Volume 87 Issue 5 November 2016 Article ID 0079 Regular
In this article, a variety of solitary wave solutions are found for some nonlinear equations. In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into the corresponding partial differential equation and the rational exp$(−\psi(\eta)$)-expansion method is implemented tofind exact solutions of nonlinear equation. We find hyperbolic, trigonometric, rational and exponential function solutions using the above equation. The results of various studies show that the suggested method is very effectiveand can be used as an alternative for finding exact solutions of nonlinear equations in mathematical physics. A comparative study with the other methods gives validity to the technique and shows that the method providesadditional solutions. Graphical representations along with the numerical data reinforce the efficacy of the procedure used. The specified idea is very effective, pragmatic for partial differential equations of fractional order andcould be protracted to other physical phenomena.
Volume 91 Issue 2 August 2018 Article ID 0028 Research Article
Nonlinear partial differential equations are the main area of focus for researchers and scientists doing research in applied mathematics. Finding solutions of these nonlinear partial differential equations had gained considerable importance over the last few decades. In this work, an analytical technique named extended exp-function method is introduced for finding archetype exact solutions of innovative nonlinear coupled Konno–Oono equation. Different types of travelling wave solutions, i.e. complex hyperbolic function and complex trigonometric function solutions, with numerous capricious parameters are revealed. Subsequently, by using Maple 16, we plot2D and 3D surfaces of analytical solutions obtained in this article. The depiction of the technique is straight, useful and can be applied to other nonlinear systems of partial differential equations.
Volume 94, 2020
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