arXiv:0909.1987 Abstract | arXiv Analytics

arXiv:0909.1987 [math.CA]Abstract References Reviews Resources

Explicit solution of the problem of equivalence for some Painleve equations

Published 2009-09-10Version 1

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.

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

Categories: math.CA, math-ph, math.MP

Subjects: 34M55, 34C14

Keywords: painleve equations, explicit solution, arbitrary ordinary second order differential, ordinary second order differential equation, equivalence

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