Artículo Original
Publicado 2013-07-29
Palabras clave
- Ecuación de Lax,
- jerarquía Brockett,
- sistema completamente integrable
Cómo citar
Felipe, R., & López Reyes, N. (2013). Integrabilidad de un sistema con doble conmutador. Revista Integración, Temas De matemáticas, 31(1), 15–23. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/3379
Resumen
Se utiliza un enfoque algebraico basado en la descomposión de grupos para mostrar la integrabilidad de un sistema de infinitas ecuacionesde Lax con doble corchete.
Descargas
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Referencias
[1] Benítez-Babilonia L., Felipe R. and López N., “Algebraic analysis of a discrete hierarchy of double bracket equations”, Differ. Equ. Dyn. Syst. 17 (2009), no. 1-2, 77–90.
[2] Bloch A.M., Brockett R.W., and Ratius T.S., “Completely integrable gradient flows”, Comm. Math. Phys. 147 (1992), 57–74.
[3] Cassidy Ph.J. and Singer M.F., “A Jordan-Holder Theorem for differential algebraic groups”, J. Algebra 328 (2011), 190–217.
[4] Dickey L.A., Soliton equations and Hamiltonian systems. Advanced Series in Mathematical Physics, 12, New Jersey, 1991.
[5] Felipe R., “Algebraic aspects of Brockett type equations”, Phys. D 132 (1999), no. 3, 287– 297.
[6] Felipe R. and Ongay F., “Super Brockett Equations: A Graded Gradient Integrable System”, Comm. Math. Phys. 220 (2001), no. 1, 95–104.
[7] Felipe R. and Ongay F., “Algebraic aspects of the discrete KP hierarchy”, Linear Algebra Appl. 338 (2001), 1–17.
[8] Kolchin E.R., Differential Algebra and Algebraic Groups. Academic Press, New York, 1976.
[9] Mulase M., “Complete integrability of the Kadomtsev-Petviashvili equation”, Adv. in Math. 54 (1984), no. 1, 57–66.
[10] Mulase M., “Algebraic theory of the KP equations,” Perspective in Mathematical Physics (ed. Penner R. and Yau S.T.), Cambridge, (1994).
[11] Schiff J., “The Camassa-Holm Equation: A Loop group approach”, Phys. D 121 (1998), no. 1-2, 24–43.
[12] Tsarev S.P., “Factorization of linear differential operators and systems”, Algebraic Theory of Differential Equations, in London Math. Soc. Lecture Note Ser. 357, Cambridge Univ. Press, Cambridge, (2009) 111–131.
[13] Semenov-Tian-Shansky M.A., Integrable Systems and Factorization Problems, Oper. Theory Adv. Appl. 141, Birkhäuser, Basel, 2003.
[14] Tam T-Y., “Gradiente flows and double bracket equations”, Differential Geom. Appl. 20 (2004), no. 2, 209–224
[2] Bloch A.M., Brockett R.W., and Ratius T.S., “Completely integrable gradient flows”, Comm. Math. Phys. 147 (1992), 57–74.
[3] Cassidy Ph.J. and Singer M.F., “A Jordan-Holder Theorem for differential algebraic groups”, J. Algebra 328 (2011), 190–217.
[4] Dickey L.A., Soliton equations and Hamiltonian systems. Advanced Series in Mathematical Physics, 12, New Jersey, 1991.
[5] Felipe R., “Algebraic aspects of Brockett type equations”, Phys. D 132 (1999), no. 3, 287– 297.
[6] Felipe R. and Ongay F., “Super Brockett Equations: A Graded Gradient Integrable System”, Comm. Math. Phys. 220 (2001), no. 1, 95–104.
[7] Felipe R. and Ongay F., “Algebraic aspects of the discrete KP hierarchy”, Linear Algebra Appl. 338 (2001), 1–17.
[8] Kolchin E.R., Differential Algebra and Algebraic Groups. Academic Press, New York, 1976.
[9] Mulase M., “Complete integrability of the Kadomtsev-Petviashvili equation”, Adv. in Math. 54 (1984), no. 1, 57–66.
[10] Mulase M., “Algebraic theory of the KP equations,” Perspective in Mathematical Physics (ed. Penner R. and Yau S.T.), Cambridge, (1994).
[11] Schiff J., “The Camassa-Holm Equation: A Loop group approach”, Phys. D 121 (1998), no. 1-2, 24–43.
[12] Tsarev S.P., “Factorization of linear differential operators and systems”, Algebraic Theory of Differential Equations, in London Math. Soc. Lecture Note Ser. 357, Cambridge Univ. Press, Cambridge, (2009) 111–131.
[13] Semenov-Tian-Shansky M.A., Integrable Systems and Factorization Problems, Oper. Theory Adv. Appl. 141, Birkhäuser, Basel, 2003.
[14] Tam T-Y., “Gradiente flows and double bracket equations”, Differential Geom. Appl. 20 (2004), no. 2, 209–224