Articles written in Pramana – Journal of Physics
Volume 78 Issue 4 April 2012 pp 513-529 Research Articles
Exact solutions of some physical models using the ($G'/G$)-expansion method
Anand Malik Fakir Chand Hitender Kumar S C Mishra
The ($G'/G$)-expansion method and its simpliﬁed version are used to obtain generalized travelling wave solutions of ﬁve nonlinear evolution equations (NLEEs) of physical importance, viz. the ($2+1$)-dimensional Maccari system, the Pochhammer–Chree equation, the Newell–Whitehead equation, the Fitzhugh–Nagumo equation and the Burger–Fisher equation. A variety of special solutions like periodic, kink–antikink solitons, bell-type solitons etc. can easily be derived from the general results. Three-dimensional proﬁle plots of some of the solutions are also drawn.
Volume 80 Issue 2 February 2013 pp 361-367 Brief Reports
Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
Hitender Kumar Anand Malik Fakir Chand
In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and $G(m, n)$ equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.
Volume 92 Issue 1 January 2019 Article ID 0008 Research Article
A dynamical study of certain nonlinear diffusion–reaction equations with a nonlinear convective flux term
ANAND MALIK HITENDER KUMAR RISHI PAL CHAHAL FAKIR CHAND
We explore the dynamics of quadratic and quartic nonlinear diffusion–reaction equations with nonlinear convective flux term, which arise in well-known physical and biological problems such as population dynamicsof the species. Three integration techniques, namely the $(G'/G)$-expansion method, its generalised version and Kudryashov method, are adopted to solve these equations. We attain new travelling and solitary wave solutions inthe form of Jacobi elliptic functions, hyperbolic functions, trigonometric functions and rational solutions with some constraint relations that naturally appear from the structure of these solutions. The travelling population fronts,which are the general solutions of nonlinear diffusion–reaction equations, describe the species invasion if higher population density corresponds to the species invasion. This effort highlights the significant features of the employed algebraic approaches and shows the diversity in the constructed solutions.
Volume 97, 2023
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