Geodesic
Virasoro symmetries of a coupled rational reduced 2D Toda hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 3, pp. 347-358 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce an interpolated coupled 2D Toda hierarchy and its symmetry reductions characterized by a rational factorization of the Lax operator. The reduced hierarchy contains several new coupled infinite-dimensional integrable hierarchies, such as the coupled bigraded Toda hierarchy, the coupled Ablowitz–Ladik hierarchy, and so on. After that, we construct additional symmetries of the coupled rational reduced 2D Toda hierarchy. These symmetries constitute a coupled Virasoro algebra and a Block Lie algebra.
Keywords: rational reductions, coupled 2D Toda hierarchy, coupled rational reduced 2D Toda hierarchy, additional symmetries. 
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Chuanzhong Li. Virasoro symmetries of a coupled rational reduced 2D Toda hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 3, pp. 347-358. http://geodesic.mathdoc.fr/item/TMF_2023_214_3_a0/

[1] M. Toda, “Vibration of chain with nonlinear interaction”, J. Phys. Soc. Japan, 22:2 (1967), 431–436 | DOI

[2] M. Toda, Nonlinear Waves and Solitons, Mathematics and its Applications (Japanese Series), 5, Kluwer, Dordrecht, 1989

[3] E. Witten, “Two-dimensional gravity and intersection theory on moduli space”, Surveys in Differential Geometry (Harvard University, Cambridge, MA, USA, April 27–29, 1990), eds. C. C. Hsiung, S. T. Yau, H. Blaine Lawson, Jr., Lehigh Univ., Bethlehem, PA, 1991, 243–310 | MR | Zbl

[4] B. A. Dubrovin, “Geometry of 2D topological field theories”, Integrable Systems and Quantum Groups (Montecatini Terme, Italy, June 14–22, 1993), Lecture Notes in Mathematics, 1620, eds. M. Francaviglia, S. Greco, Springer, Berlin, 1996, 120–348 | DOI | MR | Zbl

[5] K. Ueno, K. Takasaki, “Toda lattice hierarchy”, Group Representations and Systems of Differential Equations (University of Tokyo, December 20–27, 1982), Advanced Studies in Pure Mathematics, 4, ed. K. Okamoto, North-Holland, Amsterdam, 1984, 1–95 | DOI | MR | Zbl

[6] G. Carlet, B. A. Dubrovin, Y. Zhang, “The extended Toda hierarchy”, Mosc. Math. J., 4:2 (2004), 313–332 | DOI | MR | Zbl

[7] T. E. Milanov, “Hirota quadratic equations for the extended Toda hierarchy”, Duke Math. J., 138:1 (2007), 161–178 | DOI | MR

[8] G. Carlet, “The extended bigraded Toda hierarchy”, J. Phys. A: Math. Gen., 39:30 (2006), 9411–9435, arXiv: math-ph/0604024 | DOI | MR

[9] C. Li, “Solutions of bigraded Toda hierarchy”, J. Phys. A: Math. Theor., 44:25 (2011), 255201, 29 pp. | DOI | MR

[10] C. Li, J. He, K. Wu, Y. Cheng, “Tau function and Hirota bilinear equations for the extended bigraded Toda hierarchy”, J. Math. Phys., 51:4 (2010), 043514, 32 pp. | DOI | MR

[11] C. Z. Li, J. S. He, “Dispersionless bigraded Toda hierarchy and its additional symmetry”, Rev. Math. Phys., 24:7 (2012), 1230003, 34 pp. | DOI | MR

[12] C. Li, J. He, “The extended multi-component Toda hierarchy”, Math. Phys. Anal. Geom., 17:3–4 (2014), 377–407 | DOI | MR

[13] Chuan-Chzhun Li, Tszin-Sun Khe, “O rasshirennoi ierarkhii $Z_N$-Tody”, TMF, 185:2 (2015), 289–312, arXiv: 1403.0684 | DOI | DOI | MR

[14] A. Yu. Orlov, E. I. Schulman, “Additional symmetries for integrable equations and conformal algebra representation”, Lett. Math. Phys., 12:3 (1986), 171–179 | DOI | MR

[15] L. A. Dickey, Soliton Equations and Hamiltonian Systems, Advanced Series in Mathematical Physics, 12, World Sci., Singapore, 1991 | DOI | MR

[16] L. A. Dickey, “Additional symmetries of the Zakharov–Shabat hierarchy, string equation and isomonodromy”, Lett. Math. Phys., 44:1 (1998), 53–65 | DOI | MR

[17] B. Dubrovin, Y. Zhang, “Virasoro symmetries of the extended Toda hierarchy”, Commun. Math. Phys., 250:1 (2004), 161–193, arXiv: math/0308152 | DOI | MR

[18] C. Z. Li, J. S. He, Y. Su, “Block type symmetry of bigraded Toda hierarchy”, J. Math. Phys., 53:1 (2012), 013517, 24 pp., arXiv: 1201.1984 | DOI | MR

[19] A. Brini, G. Carlet, S. Romano, P. Rossi, “Rational reductions of the 2D-Toda hierarchy and mirror symmetry”, J. Eur. Math. Soc., 19:3 (2017), 835–880 | DOI

[20] M. J. Ablowitz, J. F. Ladik, “Nonlinear differential-difference equations”, J. Math. Phys., 16:3 (1975), 598–603 | DOI | MR

[21] J. P. Cheng, Y. Tian, Z. W. Yan, J. S. He, “The generalized additional symmetries of the two-Toda lattice hierarchy”, J. Math. Phys., 54:2 (2013), 023513, 18 pp. | DOI | MR