Reduction to the Second Painlevé Equation and N-Soliton Solutions of the Three-Dimensional Nonlinear Schrödinger Equation
1984 Volume 53 Issue 5 Pages 1634-1642
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1984 Volume 53 Issue 5 Pages 1634-1642
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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Proceedings of the Physico-Mathematical Society of Japan. 3rd Series
Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series
Tokyo Sugaku-Butsurigakukwai Kiji-Gaiyo
Tokyo Sugaku-Butsurigakkwai Hokoku
Tokyo Sugaku-Butsurigaku Kwai Kiji
