Equivalence classes and Linearization of the Riccati and Abel chain

The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular that nonlinear third order and fourth order equations from the chain are not linearizable by any point transformations....

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Bibliographic Details
Published inarXiv.org
Main Authors Ndogmo, J C, Escobar-Ruiz, Adrian M
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.12.2022
Subjects
Chains
Equivalence
Linearization
Mathematical analysis
Subgroups
Transformations (mathematics)
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Summary:The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular that nonlinear third order and fourth order equations from the chain are not linearizable by any point transformations. The Lie pseudo-group of equivalence transformations for equations of arbitrary orders from the chain are then found, together with expressions for the transformed parameter functions. An important subgroup of the group of equivalence transformations found is considered and some associated equivalence classes are exhibited.
ISSN:2331-8422