Generalized symmetries, first integrals, and exact solutions of chains of differential equations
| Autor: | C. Muriel, M. C. Nucci |
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| Rok vydání: | 2021 |
| Předmět: |
Sequence
Pure mathematics Nonlinear Sciences - Exactly Solvable and Integrable Systems Differential equation FOS: Physical sciences Mathematical Physics (math-ph) Quadrature (mathematics) Multiplier (Fourier analysis) Chain (algebraic topology) Simple (abstract algebra) Ordinary differential equation Exactly Solvable and Integrable Systems Homogeneous space Nonlinear Sciences Exactly Solvable and Integrable Systems (nlin.SI) 34A05 34C14 34C20 34G20 Nonlinear Sciences Exactly Solvable and Integrable Systems Mathematical Physics Mathematical Physics Mathematics |
| Zdroj: | Open Communications in Nonlinear Mathematical Physics. 1 |
| ISSN: | 2802-9356 |
| Popis: | 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. Comment: 16 pages |
| Databáze: | OpenAIRE |
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