Journal of Nonlinear Mathematical Physics

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Volume 18, Issue 4, December 2011, Pages 519 - 540

Generalization of an Invertible Transformation and Examples of its Applications

Authors
M. Bruschi*, †, ‖, F. Calogero*, †, **, F. Leyvraz‡, §, ††, M. Sommacal, ‡‡
*Dipartimento di Fisica, Università di Roma “La Sapienza”, 00185 Roma, Italy
†Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy
‡Departamento de Física, Universidad de los Andes, Bogotá, Colombia
§Instituto de Ciencias Físicas, UNAM, Cuernavaca, Mexico
Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France
Received 31 March 2011, Accepted 27 May 2011, Available Online 7 January 2021.
DOI
10.1142/S1402925111001751How to use a DOI?
Keywords
Explicitly invertible transformations; solvable algebraic equations; Diophantine equations; isochronous discrete-time dynamical systems; solvable systems of nonlinear PDEs; solvable nonautonomous PDEs; functional equations
Abstract

Recently we highlighted the remarkable nature of an explicitly invertible transformation, we reported some generalizations of it and examples of its expediency in several mathematical contexts: algebraic and Diophantine equations, dynamical systems (with continuous and discrete time), nonlinear PDEs, analytical geometry, functional equations. In this paper we report a significant generalization of this approach and we again illustrate via some analogous examples its expediency to identify problems which appear far from trivial but are in fact explicitly solvable.

Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - 4
Pages
519 - 540
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925111001751How to use a DOI?
Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - M. Bruschi
AU  - F. Calogero
AU  - F. Leyvraz
AU  - M. Sommacal
PY  - 2021
DA  - 2021/01/07
TI  - Generalization of an Invertible Transformation and Examples of its Applications
JO  - Journal of Nonlinear Mathematical Physics
SP  - 519
EP  - 540
VL  - 18
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001751
DO  - 10.1142/S1402925111001751
ID  - Bruschi2021
ER  -