ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
We give a general formulation of the algorithm of Fokas and Ablowitz, which then allows us to obtain transformations for nth order ordinary differential equations, to equations of the same order but perhaps of higher degree. Previously this algorithm has been used to obtain transformations for the six second order equations defining new transcendental functions discovered by Painlevé and co-workers, either to other equations in the Painlevé classification or to equations of second order and second degree. As an example of our approach we consider a new fourth order ordinary differential equation due to Cosgrove which is believed to define a new transcendent. We obtain transformations relating this equation to other fourth order ordinary differential equations, of degrees ≥2. All of these transformations, as well as the corresponding higher degree differential equations, all of which have the Painlevé property, are new. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1351886
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