The Painlevé Test of Higher Dimensional KdV Equation

1996/05/16 by Yu Song-Ju, Yu. Song-Ju, Song-Ju, Yu. +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9605003

7 pages, LaTeX

arxiv created 1996/05/16 · openalex publication_date 1996/05/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

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• A Systematic Analysis of the Properties of the Generalised Painlevé--Ince Equation
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