Numerical Solutions of Coupled Klein - Gordon - Schr dinger Equations by Finite Element Method

On the split-step method for the solution of nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative

The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations. We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative and propose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-...

Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

SOLVING FRACTIONAL NONLINEAR SCHR"{O}DINGER EQUATIONS BY FRACTIONAL COMPLEX TRANSFORM METHOD

In this paper, we apply fractional complex transform to convert the fractional nonlinear Schr"{o}dinger equations to the nonlinear Schr"{o}dinger equations.  

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION