Department Of Mathematics And Statistics

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Start date: 2016Subject: search.filters.subject.Exact solutions

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    Application of new Kudryashov method to various nonlinear partial differential equations
    (Springer, 2022-11-13T00:00:00) Malik, Sandeep; Hashemi, Mir Sajjad; Kumar, Sachin; Rezazadeh, Hadi; Mahmoud, W.; Osman, M.S.
    The purpose of this work is to seek various innovative exact solutions using the new Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This technique obtains novel exact solutions of soliton types. Moreover, several 3D and 2D plots of the higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are demonstrated by considering the relevant values of the aforementioned parameters to exhibit the nonlinear wave structures more adequately. The new Kudryashov technique is an effective, and simple technique that provides new generalized solitonic wave profiles. It is anticipated that these novel solutions will enable a thorough understanding of the development and dynamic nature of such models. � 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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    Dispersion analysis and improved F-expansion method for space–time fractional differential equations
    (Springer, 2019) Kaur, B; Gupta, R.K.
    In this article, an improved F-expansion method with the Riccati equation is suggested for space–time fractional differential equations for exact solutions. The fractional complex transformation is used to convert the space–time fractional differential equations into ordinary differential equations. The application of the method is described by solving space–time fractional potential Yu–Toda–Sasa–Fukuyama equation, and the solutions of the equation are successfully established in terms of the hyperbolic, trigonometric and rational types of functions. The graphical analysis describes the effect of fractional orders α, β, γ, δ of time and space derivatives, respectively, on the wave profile of solutions. The dispersion relation is obtained using the linear analysis, and it shows that waves follow anomalous or normal dispersion depending upon space or time fractional-order values. © 2019, Springer Nature B.V.
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    Invariants of Generalized Fifth Order Non-Linear Partial Differential Equation
    (IntechOpen, 2018) Kumar, Sachin
    The fifth order non-linear partial differential equation in generalized form is analyzed for Lie symmetries. The classical Lie group method is performed to derive similarity variables of this equation and the ordinary differential equations (ODEs) are deduced. These ordinary differential equations are further studied and some exact solutions are obtained.
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    Exact Solutions of Some Complex Non-Linear Equations," Lecture Notes in Engineering and Computer Science
    (Newswood Limited, 2018) Kumar, Sachin
    Exact solutions of the coupled Higgs and Maccari system are obtained. Travelling wave solutions of coupled Higgs equation and Maccari system in the form of Jacobi’s elliptical functions are presented.