Browsing by Author "Mathanaranjan, T."

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Approximate analytical solution to the time-fractional nonlinear Schrodinger equation through the Sumudu decomposition method.
(International Research Symposium on Pure and Applied Sciences, 2017 Faculty of Science, University of Kelaniya, Sri Lanka., 2017) Mathanaranjan, T.; Himalini, K.
The time-fractional nonlinear Schrodinger equation has the following form:.... where dV is the trapping potential and d is a real constant. The physical model of above equation and its generalized forms arise in various areas of physics, including quantum mechanics, nonlinear optics, plasma physics and superconductivity. Exact solutions of most of the fractional nonlinear Schrodinger equations cannot be found easily. Therefore, analytical and numerical methods have been used in the literature. Some of the analytical methods for solving nonlinear problems include the Adomian decomposition method, Variational iteration method and Homotopy analysis method. In this study, we use the Sumudu decomposition method to construct the approximate analytical solutions of the time-fractional nonlinear Schrodinger equations with zero and nonzero trapping potentials. The Sumudu decomposition method is a combined form of the Sumudu transform and the Adomian decomposition method. The fractional derivatives are defined in the Caputo sense. The exact solutions of some nonlinear Schrodinger equations are given as a special case of our approximate analytical solutions. The computations show that the described method is easy to apply, and it needs smaller size of computation as compared to the aforementioned existing methods. Further, the solutions are derived in a convergent series form which shows the effectiveness of the method for solving a wide variety of nonlinear fractional differential equations.
Explicit and exact traveling wave solutions for generalized Benjamin-Bona-Mahoney-Burgers equation with dual high-order nonlinear terms
(Research Symposium on Pure and Applied Sciences, 2018 Faculty of Science, University of Kelaniya, Sri Lanka, 2018) Hasna, M. T. F.; Mathanaranjan, T.
In recent years, the investigation of exact solutions to nonlinear partial differential equations has played an important role in nonlinear phenomena. Several powerful methods have been proposed to obtain exact solutions of nonlinear partial differential equations, such as the first integral method, tanh-sech method, sine-cosine method, Jacobi elliptic function method, Fexpansion method, exp-function method, expansion method and so on. The first integral method was first proposed by Feng in solving Burgers-KdV equation. It is a direct algebraic method based on the commutative algebra. Recently, it was successfully used for constructing exact solutions to a variety of nonlinear problems. Our interest in the present work is in implementing the first integral method to find the exact solution for generalized Benjamin-Bona-Mahoney-Burgers (BBMB) equation with dual high-order nonlinear terms. Considering the generalized BBMB equation with dual arbitrary power-law nonlinearity ,,