An Effective Schema for Solving Some Nonlinear Partial Differential Equation Arising In Nonlinear Physics - Baskonus, Haci Mehmet; Bulut, Hasan (Sciendo, 2015)
In this paper, a new computational algorithm called the Improved Bernoulli sub-equation function method has been proposed. This algorithm is based on the Bernoulli Sub-ODE method. Firstly, the nonlinear evaluation equations used for representing various physical phenomena are converted into ordinary differential equations by using various wave transformations. In this way, nonlinearity is preserved and represent nonlinear physical problems. The nonlinearity of physical problems together with the derivations is seen as the secret key to solve the general structure of problems. The proposed analytical schema, which is newly submitted to the literature, has been expressed comprehensively in this paper. The analytical solutions, application results, and comparisons are presented by plotting the two and three dimensional surfaces of analytical solutions obtained by using the methods proposed for some important nonlinear physical problems. Finally, a conclusion has been presented by mentioning the important discoveries in this study.
Keywords: improved Bernoulli sub-equation function method; Nonlinear Schrodinger Equation (NSE); (1+1)-dimensional nonlinear Dispersive Modified Benjamin-Bona-Mahony equation (NDMBBME); (2+1)-dimensional nonlinear cubic Klein-Gordon equation (cKGE); exponential function solution; hyperbolic function solution; complex trigonometric function solution