• Rathinasamy Sakthivel

      Articles written in Pramana – Journal of Physics

    • Travelling wave solutions for ($N + 1$)-dimensional nonlinear evolution equations

      Jonu Lee Rathinasamy Sakthivel

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      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.

    • New exact travelling wave solutions of bidirectional wave equations

      Jonu Lee Rathinasamy Sakthivel

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      The surface water waves in a water tunnel can be described by systems of the form [Bona and Chen, Physica D116, 191 (1998)] \begin{equation*}\begin{cases} v_t + u_x + (uv)_x + au_{x x x} − bv_{x x t} = 0,\\ u_t + v_x + u u_x + cv_{x x x} − d u_{x x t} = 0,\end{cases} \tag{1}\end{equation*} where 𝑎, 𝑏, 𝑐 and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modified tanh–coth function method with computerized symbolic computation.

    • Exact travelling wave solutions for some important nonlinear physical models

      Jonu Lee Rathinasamy Sakthivel

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      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.

    • New travelling wave solutions for nonlinear stochastic evolution equations

      Hyunsoo Kim Rathinasamy Sakthivel

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      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 (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.

    • Direct approach for solving nonlinear evolution and two-point boundary value problems

      Jonu Lee Rathinasamy Sakthivel

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      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.

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