Journal
COMMUNICATIONS IN THEORETICAL PHYSICS
Volume 67, Issue 2, Pages 182-188Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0253-6102/67/2/182
Keywords
exact solution; modified Riemann-Liouville derivative; space-time fractional Sharma-Tasso-Olver equation; space-time fractional potential Kadomtsev-Petviashvili equation
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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.
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