FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2163640360> ?p ?o ?g. }

• W2163640360 abstract "Abstract This paper refines existing techniques into an algorithmic method for deriving the generalization of a Lax Pair directly from a general integrable nonlinear evolution equation via the use of truncated Painleve expansions. The resulting algorithm is also applicable to multicomponent integrable systems, and is thus expected to be of great value for complicated variants of such systems in various applications areas. Although a related method has existed for simple scalar integrable evolution equations for many years now, nevertheless no systematic procedure has been given that would work in general for scalar as well as for multicomponent systems. The method presented here largely systematizes the necessary operations in applying the Painleve method to a general integrable evolution equation or system of equations. We demonstrate that by following the concept of enforcing integrability at each step (referred to here as the Principle of Integrability), one is led to an appropriate generalization of a Lax Pair, although perhaps in nonlinear form, called a “Lax Complex”. One new feature of this procedure is that it utilizes, as needed, a technique from the well-known Estabrook–Wahlquist method for determining necessary integrating factors. The end result of this procedure is to obtain a Lax Complex, whose integrability condition will contain the original evolution equation as a necessary condition. This in itself is sufficient to ensure that the Lax Complex may be used to construct Backlund solutions of the evolution equation, to obtain Darboux Transformations, and also to obtain Hirota’s tau functions, in a manner analogous to the procedure for single component systems. The additional problem of finding a general procedure for the linearization of any Lax Complex is not treated in this paper. However, we do demonstrate that a particular technique, which can be derived self-consistently from the Painleve–Backlund equations, has proven to be sufficient so far. The Nonlinear Schrodinger equation is used to illustrate the method, and then the method is applied to obtain, for the first time via the Painleve method, a Lax Complex for the vector Manakov system. Limitations in the algorithm remain, especially for cases with more than one principal branch, and these are briefly mentioned as directions for future work." @default.
• W2163640360 created "2016-06-24" @default.
• W2163640360 creator A5088511424 @default.
• W2163640360 date "2006-01-01" @default.
• W2163640360 modified "2023-09-23" @default.
• W2163640360 title "Painlevé analysis of nonlinear evolution equations—an algorithmic method" @default.
• W2163640360 cites W1510817630 @default.
• W2163640360 cites W1977199141 @default.
• W2163640360 cites W1990308921 @default.
• W2163640360 cites W1993345032 @default.
• W2163640360 cites W1998076228 @default.
• W2163640360 cites W1998795487 @default.
• W2163640360 cites W2014890512 @default.
• W2163640360 cites W2035608176 @default.
• W2163640360 cites W2035680060 @default.
• W2163640360 cites W2038082565 @default.
• W2163640360 cites W2040949612 @default.
• W2163640360 cites W2052928373 @default.
• W2163640360 cites W2063221661 @default.
• W2163640360 cites W2072259897 @default.
• W2163640360 cites W2074570375 @default.
• W2163640360 cites W2087327424 @default.
• W2163640360 cites W2090130088 @default.
• W2163640360 cites W2099235198 @default.
• W2163640360 cites W617771690 @default.
• W2163640360 doi "https://doi.org/10.1016/j.chaos.2005.02.043" @default.
• W2163640360 hasPublicationYear "2006" @default.
• W2163640360 type Work @default.
• W2163640360 sameAs 2163640360 @default.
• W2163640360 citedByCount "12" @default.
• W2163640360 countsByYear W21636403602015 @default.
• W2163640360 countsByYear W21636403602017 @default.
• W2163640360 countsByYear W21636403602020 @default.
• W2163640360 crossrefType "journal-article" @default.
• W2163640360 hasAuthorship W2163640360A5088511424 @default.
• W2163640360 hasConcept C111472728 @default.
• W2163640360 hasConcept C121332964 @default.
• W2163640360 hasConcept C134306372 @default.
• W2163640360 hasConcept C136119220 @default.
• W2163640360 hasConcept C138885662 @default.
• W2163640360 hasConcept C158622935 @default.
• W2163640360 hasConcept C172829509 @default.
• W2163640360 hasConcept C177148314 @default.
• W2163640360 hasConcept C200741047 @default.
• W2163640360 hasConcept C202444582 @default.
• W2163640360 hasConcept C2524010 @default.
• W2163640360 hasConcept C26955809 @default.
• W2163640360 hasConcept C2780586882 @default.
• W2163640360 hasConcept C28826006 @default.
• W2163640360 hasConcept C2982905333 @default.
• W2163640360 hasConcept C33923547 @default.
• W2163640360 hasConcept C57691317 @default.
• W2163640360 hasConcept C62520636 @default.
• W2163640360 hasConceptScore W2163640360C111472728 @default.
• W2163640360 hasConceptScore W2163640360C121332964 @default.
• W2163640360 hasConceptScore W2163640360C134306372 @default.
• W2163640360 hasConceptScore W2163640360C136119220 @default.
• W2163640360 hasConceptScore W2163640360C138885662 @default.
• W2163640360 hasConceptScore W2163640360C158622935 @default.
• W2163640360 hasConceptScore W2163640360C172829509 @default.
• W2163640360 hasConceptScore W2163640360C177148314 @default.
• W2163640360 hasConceptScore W2163640360C200741047 @default.
• W2163640360 hasConceptScore W2163640360C202444582 @default.
• W2163640360 hasConceptScore W2163640360C2524010 @default.
• W2163640360 hasConceptScore W2163640360C26955809 @default.
• W2163640360 hasConceptScore W2163640360C2780586882 @default.
• W2163640360 hasConceptScore W2163640360C28826006 @default.
• W2163640360 hasConceptScore W2163640360C2982905333 @default.
• W2163640360 hasConceptScore W2163640360C33923547 @default.
• W2163640360 hasConceptScore W2163640360C57691317 @default.
• W2163640360 hasConceptScore W2163640360C62520636 @default.
• W2163640360 hasLocation W21636403601 @default.
• W2163640360 hasOpenAccess W2163640360 @default.
• W2163640360 hasPrimaryLocation W21636403601 @default.
• W2163640360 hasRelatedWork W1964781732 @default.
• W2163640360 hasRelatedWork W1969481295 @default.
• W2163640360 hasRelatedWork W1987371472 @default.
• W2163640360 hasRelatedWork W1992592519 @default.
• W2163640360 hasRelatedWork W2000071128 @default.
• W2163640360 hasRelatedWork W2006961398 @default.
• W2163640360 hasRelatedWork W2089796306 @default.
• W2163640360 hasRelatedWork W2351859806 @default.
• W2163640360 hasRelatedWork W2371896326 @default.
• W2163640360 hasRelatedWork W4239376463 @default.
• W2163640360 isParatext "false" @default.
• W2163640360 isRetracted "false" @default.
• W2163640360 magId "2163640360" @default.
• W2163640360 workType "article" @default.