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Painlevé Analysis for (2 + 1) Dimensional Non-Linear Schrödinger Equation
College of Mathematics, China University of Mining and Technology, Xuzhou, China
College of Mathematics, China University of Mining and Technology, Xuzhou, China
- 1 College of Mathematics, China University of Mining and Technology, Xuzhou, China
- 2 College of Mathematics, China University of Mining and Technology, Xuzhou, China
Applied Mathematics·Volume 08 (2017)·Pages 1539–1545·Published 1 November 2017·DOI10.4236/am.2017.811112
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Abstract
This paper investigates a real version of a (2 + 1) dimensional nonlinear Schr ? dinger equation through adoption of Painlevé test by means of which the (2 + 1) dimensional nonlinear Schr ? dinger equation is studied according to the Weiss et al . method and Kruskal’s simplification algorithms. According to Painlevé test, it is found that the number of arbitrary functions required for explaining the Cauchy-Kovalevskaya theorem exist. Finally, the associated B ? cklund transformation and bilinear form is directly obtained from the Painlevé test.
Keywords(2 + 1) Dimensional Nonlinear Schrödinger EquationPainlevéAnalysisBäcklund TransformationBilinear Form
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