Аннотация:
Third-order ordinary differential equations with Lie symmetry algebras isomorphic to the nonsolvable algebra sl(2,R) admit solvable structures. These solvable structures can be constructed by using the basis elements of these algebras. Once the solvable structures are known, the given equation can be integrated by quadratures as in the case of solvable symmetry algebras.
Ключевые слова:
first integral; solvable structure; C∞-symmetry; nonsolvable algebra.
Финансовая поддержка
This research was partially supported by the University of Cádiz and Junta de Andalucía research group FQM 377. A. Ruiz acknowledges the support of a grant of the University of Cádiz program “Movilidad Internacional, Becas UCA-Internacional-Posgrado” during his stay at the University of Minnesota.
Поступила:11 ноября 2015 г.; в окончательном варианте 3 августа 2016 г.; опубликована 8 августа 2016 г.
Adrián Ruiz, Concepción Muriel, Tutorials, Schools, and Workshops in the Mathematical Sciences, Groups, Invariants, Integrals, and Mathematical Physics, 2023, 141
Ruiz A., Muriel C., “On the Integrability of Gl(2,Double-Struck Capital R)-Invariant Fourth-Order Ordinary Differential Equations”, Math. Meth. Appl. Sci., 2021
A. Ruiz, C. Muriel, SEMA SIMAI Springer Series, 9, Recent Advances in Differential Equations and Control Theory, 2021, 83
P. Morando, C. Muriel, A. Ruiz, “First integrals of differential operators from sl(2, R) symmetries”, Mathematics, 8:12 (2020), 2167
A. Ruiz, C. Muriel, J. Ramírez, RSME Springer Series, 4, Recent Advances in Pure and Applied Mathematics, 2020, 93
A. Ruiz, C. Muriel, J. Ramirez, “Exact general solution and first integrals of a remarkable static Euler-Bernoulli beam equation”, Commun. Nonlinear Sci. Numer. Simul., 69 (2019), 261–269
A. Ruiz, C. Muriel, “Involutive pairs of lambda-symmetries for nth-order ordinary differential equations”, J. Comput. Appl. Math., 354 (2019), 562–568
P. Morando, C. Muriel, A. Ruiz, “Generalized solvable structures and first integrals for odes admitting an symmetry algebra”, J. Nonlinear Math. Phys., 26:2 (2019), 188–201
Ruiz A., Muriel C., “Construction of solvable structures from so(3, C)”, Springer Proceedings in Mathematics and Statistics, 266, 2018, 53-65
A. Ruiz, C. Muriel, Springer Proceedings in Mathematics & Statistics, 266, Symmetries, Differential Equations and Applications, 2018, 53
A. Ruiz, C. Muriel, “First integrals and parametric solutions of third-order ODEs admitting sl(2,R)”, J. Phys. A-Math. Theor., 50:20 (2017), 205201
Цитирование в формате AMSBIB
Обратная связь: