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This article is cited in 7 scientific papers (total in 7 papers)
Ermakov–Pinney and Emden–Fowler equations: New solutions from novel Bäcklund transformations
S. Carilloab, F. Zulloc a Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Università di Roma "La
Sapienza". Roma, Italy
b Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Roma, Italy
c Brescia, Italy
Abstract:
We study the class of nonlinear ordinary differential equations $y''y= F(z,y^2)$, where $F$ is a smooth function. Various ordinary differential equations with a well-known importance for applications belong to this class of nonlinear ordinary differential equations. Indeed, the Emden–Fowler equation, the Ermakov–Pinney equation, and the generalized Ermakov equations are among them. We construct Bäcklund transformations and auto-Bäcklund transformations: starting from a trivial solution, these last transformations induce the construction of a ladder of new solutions admitted by the given differential equations. Notably, the highly nonlinear structure of this class of nonlinear ordinary differential equations implies that numerical methods are very difficult to apply.
Keywords:
nonlinear ordinary differential equation, Bäcklund transformation, Schwarzian derivative, Ermakov–Pinney equation, Emden–Fowler equation.
Received: 12.11.2017
Citation:
S. Carillo, F. Zullo, “Ermakov–Pinney and Emden–Fowler equations: New solutions from novel Bäcklund transformations”, TMF, 196:3 (2018), 373–389; Theoret. and Math. Phys., 196:3 (2018), 1268–1281
Linking options:
https://www.mathnet.ru/eng/tmf9508https://doi.org/10.4213/tmf9508 https://www.mathnet.ru/eng/tmf/v196/i3/p373
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Abstract page: | 415 | Full-text PDF : | 144 | References: | 31 | First page: | 19 |
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