Ferapontov, E. V.; Khusnutdinova, K. R.; Pavlov, M. V. Classification of integrable \((2+1)\)-dimensional quasilinear hierarchies. (English) Zbl 1178.37072 Theor. Math. Phys. 144, No. 1, 907-915 (2005); translation from Teor. Mat. Fiz. 144, No. 1, 35-43 (2005). Summary: We investigate the \((2+1)\)-dimensional hierarchies associated with the integrable PDEs of the form \(\Delta _{tt} = F(\Delta _{xx}, \Delta _{xt}, \Delta _{xy})\), which generalize the dispersionless KP hierarchy. Integrability is understood as the existence of infinitely many hydrodynamic reductions. Cited in 15 Documents MSC: 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35C05 Solutions to PDEs in closed form Keywords:hydrodynamic reductions; pseudopotentials × Cite Format Result Cite Review PDF Full Text: DOI Link References: [1] I. Krichever, A. Marshakov, and A. Zabrodin, ”Integrable structure of the Dirichlet boundary problem in multiply-connected domains,” hep-th/0309010 (2003). · Zbl 1091.37019 [2] M. V. Pavlov, Russ. Math. Surveys, 58, No.2, 384–385 (2003); Theor. Math. Phys., 138, 45–58 (2004). · Zbl 1056.37082 · doi:10.1070/RM2003v058n02ABEH000620 [3] V. M. Buchstaber, D. V. Leykin, and M. V. Pavlov, Funct. Anal. Appl., 37, 251–262 (2003). · Zbl 1075.37527 · doi:10.1023/B:FAIA.0000015576.05085.bc [4] J. Gibbons and S. P. Tsarev, Phys. Lett. A, 211, 19–24 (1996); 258, 263–270 (1999). · Zbl 1072.35588 · doi:10.1016/0375-9601(95)00954-X [5] R. Carroll and Yu. Kodama, J. Phys. A, 28, 6373–6387 (1995). · Zbl 0876.35101 · doi:10.1088/0305-4470/28/22/013 [6] E. V. Ferapontov and K. R. Khusnutdinova, Comm. Math. Phys., 248, 187–206 (2004); J. Phys. A, 37, 2949–2963 (2004); J. Math. Phys., 45, 2365–2377 (2004). · Zbl 1070.37047 · doi:10.1007/s00220-004-1079-6 [7] M. Manas, L. M. Alonso, and E. Medina, J. Phys. A, 35, 401–417 (2002). · Zbl 1040.37057 · doi:10.1088/0305-4470/35/2/316 [8] J. Chazy, C. R. Acad. Sci. Paris, 150, 456–458 (1910). [9] M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Wiley, New York (1984). · Zbl 0643.33001 [10] E. V. Zakharov, ”Dispersionless limit of integrable systems in 2+1 dimensions,” in: Singular Limits of Dispersive Waves (NATO ASI Ser., Ser. B Phys., Vol. 320, N. M. Ercolani, I. R. Gabitov, C. D. Levermore, and D. Serre, eds.), Plenum, New York (1994), pp. 165–174. · Zbl 0852.35130 [11] S. P. Tsarev, Sov. Math. Dokl., 31, 488–491 (1985); Math. USSR Izv., 37, 397–419 (1991). [12] C. P. Boyer and J. D. Finley, J. Math. Phys., 23, 1126–1130 (1982). · Zbl 0484.53051 · doi:10.1063/1.525479 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.