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

抄録

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.