Explicit solution of the problem of equivalence for some Painleve equations

2009/09/10 by V. V. Kartak, Kartak, V. V.
Mathematics · Physics and Astronomy · #34C14 #34M55 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP #msc:34C14 #msc:34M55

paper · pdf · doi:10.48550/arxiv.0909.1987

11 pages. Ufa Math Journal, No 3, 2009 (accepted)

arxiv created 2009/09/10 · arxiv updated 2009/12/01

Abstract

For an arbitrary ordinary second order differential equation a test is constructed that checks if this equation is equivalent to Painleve I, II or Painleve III with three zero parameters equations under the substitutions of variables. If it is true then in case the Painleve equations I and II an explicite change of variables is given that is written using the differential invariants of the equation.

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