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Abstract: By means of Power Geometry, shortly described in §1, in the generic case we compute all power expansions of solutions to the sixth Painleve' equation at points x = 0, x = ∞ (§2) and x = 1 (§3). Three symmetries of the equation allow reducing all these expansions to three basic families. One of them begins by the term with arbitrary power exponent that means a new type of singularity of the equation.Note: Research direction:Mathematical problems and theory of numerical method
Abstract: We consider an ordinary differential equation (ODE) which can be written as a po...
Abstract: Here are written methods and results of power geometry which are used to resear...
We study the general sixth Painleve ́ equation, develop, and justify the existence of several groups...
Abstract: We consider the sixth Painlev'e equation in the case a,b ≠ 0. By the methods of ...
Abstract: Using Power Geometry [1,2],in the generic case we find all expansion of solution...
Abstract: We consider the sixth Painleve equation for a=0. For the case we obtain six new ...
Abstract: By means of Power Geometry, shortly presented in §1, in the generic case we comp...
Abstract: We obtain all asymptotic expansions of solutions to the sixth Painlev'e equation...
Abstract: To the sixth Painleve equation near three its singular points for various value...
Abstract: The article is devoted to the study of the fifth Painleve equation. The aim of t...
Abstract: We compute all power expansions of solutions to the first Painleve equation by t...
Abstract: Here we consider the sixth Painlev'e equation for all values of four its complex...
Abstract: Here are the history of origin of the problem, short review of works, formulatin...
Abstract: We consider an ordinary differential equation of the fourth order, which is the ...
Abstract: The purpose of this work is to clarify the question: can solutions to the sixth ...
Abstract: We consider an ordinary differential equation (ODE) which can be written as a po...
Abstract: Here are written methods and results of power geometry which are used to resear...
We study the general sixth Painleve ́ equation, develop, and justify the existence of several groups...
Abstract: We consider the sixth Painlev'e equation in the case a,b ≠ 0. By the methods of ...
Abstract: Using Power Geometry [1,2],in the generic case we find all expansion of solution...
Abstract: We consider the sixth Painleve equation for a=0. For the case we obtain six new ...
Abstract: By means of Power Geometry, shortly presented in §1, in the generic case we comp...
Abstract: We obtain all asymptotic expansions of solutions to the sixth Painlev'e equation...
Abstract: To the sixth Painleve equation near three its singular points for various value...
Abstract: The article is devoted to the study of the fifth Painleve equation. The aim of t...
Abstract: We compute all power expansions of solutions to the first Painleve equation by t...
Abstract: Here we consider the sixth Painlev'e equation for all values of four its complex...
Abstract: Here are the history of origin of the problem, short review of works, formulatin...
Abstract: We consider an ordinary differential equation of the fourth order, which is the ...
Abstract: The purpose of this work is to clarify the question: can solutions to the sixth ...
Abstract: We consider an ordinary differential equation (ODE) which can be written as a po...
Abstract: Here are written methods and results of power geometry which are used to resear...
We study the general sixth Painleve ́ equation, develop, and justify the existence of several groups...
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