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KIAM Preprint  70, Moscow, 2007
Authors: Bruno A. D., Goryuchkina I. V.
All asymptotic expansions of solutions to the equation P6 in the case ab=0
Here we consider the equation P6 for x→0 and a=0. In that, we obtained 4 base families of expansions of its solutions different from base families of expansions of solutions for ab≠0. Altogether for x→0 and a=0 there exist 11 families of expansions of solutions involving expansions of four types: power, power-logarithmic, complicated and exotic. Most of them are new. Cases a=0, x→∞ and b=0 are obtained from the case a=0, x→0 by means of reflections of symmetries of the equation. For a=b=0 there are absent expansions of solutions different from expansions of solutions for ab≠0, a=0 and b=0. The last paragraph is dedicated to comparison of obtained results with known results.
Publication language: russian,  pages: 30
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Bruno Alexander Dmitrievich, RAS
  • Goryuchkina I. V.,  KIAM RAS