Articles written in Pramana – Journal of Physics
Volume 75 Issue 4 October 2010 pp 565-578 Research Articles
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ($N + 1$)-dimensional nonlinear evolution equations. Four models, the ($N + 1$)-dimensional generalized Boussinesq equation, ($N + 1$)-dimensional sine-cosine-Gordon equation, ($N + 1$)-double sinh-Gordon equation and ($N + 1$)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Volume 76 Issue 6 June 2011 pp 819-829
The surface water waves in a water tunnel can be described by systems of the form [Bona and Chen,
Volume 80 Issue 5 May 2013 pp 757-769
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
Volume 80 Issue 6 June 2013 pp 917-931
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the $(G'/G)$-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic Broer–Kaup equation and stochastic coupled Korteweg–de Vries (
Volume 81 Issue 6 December 2013 pp 893-909
Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples including time-delayed nonlinear Burgers equation to illustrate the validity and the great potential of the differential transform method. Numerical experiments demonstrate the use and computational efﬁciency of the method. This method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work.
Volume 96, 2022
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