TY - JOUR
T1 - Generalization of an invertible transformation and examples of its applications
AU - Bruschi, Mario
AU - Calogero, Francesco
AU - Leyvraz, François
AU - Sommacal, Matteo
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - explicitly invertible transformations
KW - solvable algebraic equations
KW - Diophantine equations
KW - isochronous discrete-time dynamical systems
KW - solvable systems of nonlinear PDEs
KW - solvable nonautonomous PDEs
KW - functional equations
U2 - 10.1142/S1402925111001751
DO - 10.1142/S1402925111001751
M3 - Article
VL - 18
SP - 519
EP - 540
JO - Journal of Nonlinear Mathematical Physics
JF - Journal of Nonlinear Mathematical Physics
SN - 1402-9251
IS - 04
ER -