Integrable Abel Equations and Vein's Abel Equation

S.C. Mancas; Haret C. Rosu; Stefani Mancas

doi:10.1002/mma.3575

Integrable Abel Equations and Vein's Abel Equation

S.C. Mancas, Haret C. Rosu, Stefani Mancas

Research output: Contribution to journal › Article › peer-review

Abstract

We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein’s Abel equation whose solutions are expressed in terms of the third order hyperbolic functions and a phase space analysis of the corresponding nonlinear oscillator is also provided.

Original language	American English
Journal	Mathematical Methods in the Applied Sciences
Volume	39
DOIs	https://doi.org/10.1002/mma.3575
State	Published - Apr 1 2016

Keywords

Abel equation
Appell invariant
normal form
canonical form
third order hyperbolic function

Disciplines

Mathematics

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10.1002/mma.3575License: CC BY

Integrable Abel Equations and Veins Abel EquationFinal published version, 531 KBLicense: CC BY

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title = "Integrable Abel Equations and Vein's Abel Equation",

abstract = " We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein{\textquoteright}s Abel equation whose solutions are expressed in terms of the third order hyperbolic functions and a phase space analysis of the corresponding nonlinear oscillator is also provided.",

keywords = "Abel equation, Appell invariant, normal form, canonical form, third order hyperbolic function",

author = "S.C. Mancas and Rosu, {Haret C.} and Stefani Mancas",

year = "2016",

month = apr,

day = "1",

doi = "10.1002/mma.3575",

language = "American English",

volume = "39",

journal = "Mathematical Methods in the Applied Sciences",

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TY - JOUR

T1 - Integrable Abel Equations and Vein's Abel Equation

AU - Mancas, S.C.

AU - Rosu, Haret C.

AU - Mancas, Stefani

PY - 2016/4/1

Y1 - 2016/4/1

N2 - We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein’s Abel equation whose solutions are expressed in terms of the third order hyperbolic functions and a phase space analysis of the corresponding nonlinear oscillator is also provided.

AB - We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein’s Abel equation whose solutions are expressed in terms of the third order hyperbolic functions and a phase space analysis of the corresponding nonlinear oscillator is also provided.

KW - Abel equation

KW - Appell invariant

KW - normal form

KW - canonical form

KW - third order hyperbolic function

UR - https://commons.erau.edu/publication/590

U2 - 10.1002/mma.3575

DO - 10.1002/mma.3575

M3 - Article

SN - 1099-1476

VL - 39

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

ER -

Integrable Abel Equations and Vein's Abel Equation

Abstract

Keywords

Disciplines

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