Matches in SemOpenAlex for { <https://semopenalex.org/work/W23144021> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W23144021 abstract "The Painleve singularity analysis is one of the systematic and powerful method to identify the integrability conditions of nonlinear partial differential equations (NPDEs). In recent years, this method has been applied to a very large number of NPDEs and systematically established the complete integrability properties like Lax pair, Backlund, Darboux and Miura transformations, bilinear transformation, soliton solutions and so on. In the last decade of the nineteenth century some mathematicians focused their attention on the classification of ordinary differential equations (ODEs) on the basis of the type of singularity their of solutions. It is essential to distinguish between two types of singularities. Fixed singularities determined by the coefficients of the equation and its location do not therefore depend on initial conditions. Movable singularities are such whose location on the complex plane does indeed depend on the initial conditions. The beginning of the study of singularities in the complex plane for differential equations was always attributed to Cauchy, whose idea was to consider local solutions on the complex plane and to use methods of analytical continuation to obtain general solutions. For this procedure to work a complete knowledge of singularities of the equation and its location in the complex plane is required. Some French mathematicians (Painleve, Gambier, Garnier and Chazy), following the ideas of Fuchs, Kovalevskaya, Picard and other, completely classified first order equations and studied second order differential equations. In this case, Paul Painleve [1] found 50 types of second order equations whose only movable singularities were ordinary poles. This special analytical property now carries his name and in what follow will be referred to as the Painleve Property (PP). Of these 50 types of equations 44 can be integrated in terms of known functions (Riccati equations, elliptic functions, linear equations) and the other six in spite of having meromorphic solutions do not have algebraic integrals that would allow to reduce the equation to quadratures. Today these are known as Painleve Transcendents: P1 : w′′(z) = 6w2(z) + az; P2 : w′′(z) = 2w3(z) + zw(z) + b; P3 : w′′(z) = w′2" @default.
- W23144021 created "2016-06-24" @default.
- W23144021 creator A5052060731 @default.
- W23144021 date "2002-01-01" @default.
- W23144021 modified "2023-09-27" @default.
- W23144021 title "PP-Test for Integrability of Some Evolution Differential Equations" @default.
- W23144021 cites W1507850137 @default.
- W23144021 cites W2480312583 @default.
- W23144021 hasPublicationYear "2002" @default.
- W23144021 type Work @default.
- W23144021 sameAs 23144021 @default.
- W23144021 citedByCount "0" @default.
- W23144021 crossrefType "journal-article" @default.
- W23144021 hasAuthorship W23144021A5052060731 @default.
- W23144021 hasConcept C121332964 @default.
- W23144021 hasConcept C12843 @default.
- W23144021 hasConcept C134306372 @default.
- W23144021 hasConcept C158622935 @default.
- W23144021 hasConcept C16171025 @default.
- W23144021 hasConcept C17825722 @default.
- W23144021 hasConcept C179117685 @default.
- W23144021 hasConcept C2524010 @default.
- W23144021 hasConcept C33923547 @default.
- W23144021 hasConcept C51544822 @default.
- W23144021 hasConcept C62520636 @default.
- W23144021 hasConcept C78045399 @default.
- W23144021 hasConceptScore W23144021C121332964 @default.
- W23144021 hasConceptScore W23144021C12843 @default.
- W23144021 hasConceptScore W23144021C134306372 @default.
- W23144021 hasConceptScore W23144021C158622935 @default.
- W23144021 hasConceptScore W23144021C16171025 @default.
- W23144021 hasConceptScore W23144021C17825722 @default.
- W23144021 hasConceptScore W23144021C179117685 @default.
- W23144021 hasConceptScore W23144021C2524010 @default.
- W23144021 hasConceptScore W23144021C33923547 @default.
- W23144021 hasConceptScore W23144021C51544822 @default.
- W23144021 hasConceptScore W23144021C62520636 @default.
- W23144021 hasConceptScore W23144021C78045399 @default.
- W23144021 hasLocation W231440211 @default.
- W23144021 hasOpenAccess W23144021 @default.
- W23144021 hasPrimaryLocation W231440211 @default.
- W23144021 hasRelatedWork W1592727869 @default.
- W23144021 hasRelatedWork W1831216351 @default.
- W23144021 hasRelatedWork W1970520790 @default.
- W23144021 hasRelatedWork W1977179965 @default.
- W23144021 hasRelatedWork W1997629820 @default.
- W23144021 hasRelatedWork W2030266977 @default.
- W23144021 hasRelatedWork W2030648974 @default.
- W23144021 hasRelatedWork W2046351603 @default.
- W23144021 hasRelatedWork W2070044326 @default.
- W23144021 hasRelatedWork W2072797017 @default.
- W23144021 hasRelatedWork W2073484365 @default.
- W23144021 hasRelatedWork W2141150708 @default.
- W23144021 hasRelatedWork W2331012991 @default.
- W23144021 hasRelatedWork W2361457645 @default.
- W23144021 hasRelatedWork W2899654464 @default.
- W23144021 hasRelatedWork W2963854264 @default.
- W23144021 hasRelatedWork W3083404220 @default.
- W23144021 hasRelatedWork W3098872604 @default.
- W23144021 hasRelatedWork W650874852 @default.
- W23144021 hasRelatedWork W3147751858 @default.
- W23144021 isParatext "false" @default.
- W23144021 isRetracted "false" @default.
- W23144021 magId "23144021" @default.
- W23144021 workType "article" @default.