Journal of the Physical Society of Japan
Online ISSN : 1347-4073
Print ISSN : 0031-9015
ISSN-L : 0031-9015
On Reductions to the Second Painlevé Equation and N-Soliton Solutions of the Two and Three Dimensional Nonlinear Klein-Gordon Equations
Masayoshi Tajiri
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1984 Volume 53 Issue 1 Pages 1-4

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Abstract
The two and three-dimensional nonlinear Klein-Gordon (and Higgs) equations are reduced to the one-dimensional nonlinear Schrödinger equation. N-soliton solutions of the two and three-dimensional nonlinear Klein-Gordon (and Higgs) equations are obtained by substituting N-soliton solutions of the one-dimensional nonlinear Schrödinger equation into the similarity transformations. It is also shown that the two and three-dimensional Higgs equations can be reduced to the second Painlevé equation.
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