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The Painlevé Test of Higher Dimensional KdV Equation

Yu. Song-Ju·T. Fukuyama
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Abstract

We argue the integrability of the generalized KdV(GKdV) equation using the Painlevé test. For $d( \le 2)$ dimensional space, GKdV equation passes the Painlevé test but does not for $d \geq 3$ dimensional space. We also apply the Ablowitz-Ramani-Segur's conjecture to the GKdV equation in order to complement the Painlevé test.

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Yu. Song-Ju, T. Fukuyama. 1996-05-16. The Painlevé Test of Higher Dimensional KdV Equation. https://arxiv.org/abs/solv-int/9605003

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