C. Muriel ; M. C. Nucci - Generalized symmetries, first integrals, and exact solutions of chains of differential equations

ocnmp:7360 - Open Communications in Nonlinear Mathematical Physics, June 15, 2021, Volume 1 - https://doi.org/10.46298/ocnmp.7360
Generalized symmetries, first integrals, and exact solutions of chains of differential equations

Authors: C. Muriel ; M. C. Nucci

New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied. The determination of n generalized symmetries of the nth-order equation in each chain provides, without any kind of integration, n-1 functionally independent first integrals of the equation. A remaining first integral arises by a quadrature by using a Jacobi last multiplier that is expressed in terms of the preceding equation in the corresponding sequence. The complete set of n first integrals is used to obtain the exact general solution of the nth-order equation of each sequence. The results are applied to derive directly the exact general solution of any equation in the Riccati and Abel chains.


Volume: Volume 1
Published on: June 15, 2021
Accepted on: June 15, 2021
Submitted on: April 14, 2021
Keywords: Nonlinear Sciences - Exactly Solvable and Integrable Systems,Mathematical Physics,34A05, 34C14, 34C20, 34G20


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