Reduction to the Second Painlevé Equation and N-Soliton Solutions of the Three-Dimensional Nonlinear Schrödinger Equation

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  • Tajiri Masayoshi
    Department of Mathematical Sciences, College of Engineering, University of Osaka Prefecture
  • Hagiwara Mari
    Department of Mathematical Sciences, College of Engineering, University of Osaka Prefecture

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  • Reduction to the Second Painleve Equation and N-Soliton Solutions of the Three-Dimensional Nonlinear Schrodinger Equation
  • Reduction to the Second Painleve Equati

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Abstract

The three-dimensional nonlinear Schrödinger (3D-NLS) equation is reduced first to the 2D-Klein-Gordon equation, secondly to the 1D-NLS equation and finally to the second Painlevé equation by similarity transformations. It is also shown that the 3D-NLS equation has N-soliton solutions which are not parallel propagating solutions.

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