Dark Soliton Solutions of Space-Time Fractional SharmaTassoOlver and Potential KadomtsevPetviashvili Equations

GÜNER Ö., KORKMAZ A., Bekir A.

COMMUNICATIONS IN THEORETICAL PHYSICS, vol.67, no.2, pp.182-188, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1088/0253-6102/67/2/182
  • Journal Name: COMMUNICATIONS IN THEORETICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.182-188
  • Eskisehir Osmangazi University Affiliated: Yes

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.