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Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests

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Abstract

It is shown that the two-dimensional sine-Gordon equation does not satisfy the necessary conditions of the Painlevé conjecture to be solvable by inverse scattering since it is reducible to an ordinary differential equation which has a movable logarithmic branch point and so is not of Painlevé type.

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Clarkson, P.A. Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests. Lett Math Phys 10, 297–299 (1985). https://doi.org/10.1007/BF00420570

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Keywords

  • Differential Equation
  • Statistical Physic
  • Ordinary Differential Equation
  • Group Theory
  • Branch Point