Dark Soliton Solutions of Space-Time Fractional Sharma–Tasso–Olver and Potential Kadomtsev–Petviashvili Equations. (February 2017)

• Record Type: Journal Article
• Authors: Guner, Ozkan; Korkmaz, Alper; Bekir, Ahmet
• Is Part Of: Communications in theoretical physics. Volume 67:Number 2(2017:Feb.)
• Publication Date: 2017-02
• Subjects: exact solution -- modified Riemann–Liouville derivative -- space-time fractional Sharma–Tasso–Olver equation -- space-time fractional potential Kadomtsev–Petviashvili equation; 04.20.Jb -- 94.05.Fg -- 02.30.Jr; Physics -- Periodicals; 530.105
• DOI: 10.1088/0253-6102/67/2/182
• Languages: English
• ISSNs: 0253-6102

Abstract

Abstract: Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.