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- Title
Expansions of solutions to the fifth Painlevé equation near its nonsingular point.
- Authors
Bruno, A.; Parusnikova, A.
- Abstract
The article focuses on the expansions of solutions in the nonsingular point to the fifth Painlevé equation with three Laurent series expansions, and seven Taylor series expansions. It considers the fifth é equation with α, β, γ, and δ as complex parameters, and w and z as the dependent and independent complex variables. It states that the asymptotic expansions of solutions (AES) on the nonsingular point of Painlevé equation were found using the method of two-dimensional power geometry. Moreover, it presents theorems regarding the convergence and results of the expansions.
- Subjects
PAINLEVE equations -- Numerical solutions; TAYLOR'S series; LAURENT series; ARBITRARY constants; GEOMETRY; STOCHASTIC convergence; MATHEMATICS theorems; OPERATOR product expansions; COMPLEX numbers
- Publication
Doklady Mathematics, 2012, Vol 85, Issue 1, p87
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562412010292