Integrable Equations of the Dispersionless Hirota type and Hypersurfaces in the Lagrangian Grassmannian
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Ablowitz, 2006, “Integrable systems and modular forms of level 2”, Journal of Physics A: Mathematical and General, 39, 15341, 10.1088/0305-4470/39/50/003
Atiyah, 1978, “Self-duality in four-dimensional Riemannian geometry”, Proceedings of the Royal Society of London, Series, 425, 10.1098/rspa.1978.0143
Akivis, 1999, “Semiintegrable almost Grassmann structures”, Differential Geometry and Its Applications, 10, 257, 10.1016/S0926-2245(99)00014-5
Bailey, 1991, “Complex paraconformal manifolds – their differential geometry and twistor theory”, Forum Mathematicum, 3, 61, 10.1515/form.1991.3.61
Banos, 2003, “On symplectic classification of effective 3-forms and Monge-Ampére equations”, Differential Geometry and Its Applications, 19, 147, 10.1016/S0926-2245(03)00017-2
Bertram, 1996, “Un theoréme de Liouville pour les algébres de Jordan”, Bulletin de la Société Mathématique de France, 124, 299, 10.24033/bsmf.2282
Bobienski, 2007, “Irreducible SO(3) geometry in dimension five”, Journal für die Reine und Angewandte Mathematik, 605, 51
Bogdanov, 2005, “On dispersionless BKP hierarchy and its reductions”, Journal of Nonlinear Mathematical Physics, 12, 64, 10.2991/jnmp.2005.12.s1.6
Boyarsky, 2001, “Associativity equations in dispersionless integrable hierarchies”, Physics Letters, B 515, 483, 10.1016/S0370-2693(01)00893-0
Boyer, 1982, “Killing vectors in self-dual Euclidean Einstein spaces”, Journal of Mathematical Physics, 23, 1126, 10.1063/1.525479
Braden, 2002, “WDVV equations as functional relations”, Physics Letters, B 451, 376, 10.1016/S0370-2693(02)02225-6
Buchstaber, 2003, “The Egorov hydrodynamic chains, the Chazy equation and SL(2, C)group”, Functional Analysis and Its Applications, 37, 13, 10.1023/B:FAIA.0000015576.05085.bc
Burovskii, 2008, “Second order quasilinear PDEs and conformal structures in projective space”
Calabi, 1958, “Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jorgens”, Michigan Mathematical Journal, 5, 105, 10.1307/mmj/1028998055
Carroll, 1995, “Solution of the dispersionless Hirota equations”, Journal of Physics, A 28, 6373
Cartan, 1909, “Les groupes de transformations continus, infinis, simples”, Annales Scientifiques de l'École Normale Supérieure, 26, 93, 10.24033/asens.603
Doubrov, “Contact Trivialization of Ordinary Differential Equations”, Differential Geometry and Its Applications, 73
Dunajski, 2001, “Einstein-Weyl geometry, the dKP equation and twistor theory”, Journal of Geometry and Physics, 37, 63, 10.1016/S0393-0440(00)00033-4
Dunajski, 2006, “Paraconformal geometry of nth-order ODEs, and exotic holonomy in dimension four”, Journal of Geometry and Physics, 56, 1790, 10.1016/j.geomphys.2005.10.007
Ferapontov, 2004, “On the integrability of (2+1)-dimensional quasilinear systems”, Communications in Mathematical Physics, 248, 187, 10.1007/s00220-004-1079-6
Ferapontov, 2004, “The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type”, Journal of Physics A: Mathematical and General, 37, 2949, 10.1088/0305-4470/37/8/007
Ferapontov, 2002, “Boyer-Finley equation and systems of hydrodynamic type”, Classical and Quantum Gravity, 19, L205, 10.1088/0264-9381/19/24/101
Ferapontov, 2003, “Hydrodynamic reductions of the heavenly equation”, Classical and Quantum Gravity, 20, 2429, 10.1088/0264-9381/20/11/331
Ferapontov, 2004, “Hydrodynamic reductions of multi-dimensional dispersionless PDEs: the test for integrability”, Journal of Mathematical Physics, 45, 2365, 10.1063/1.1738951
Ferapontov, 2005, “Classification of integrable (2+1)-dimensional quasilinear hierarchies”, Theoretical and Mathematical Physics, 144, 35, 10.1007/s11232-005-0117-7
Gibbons, 1996, “Reductions of the Benney equations”, Physics Letters, A 211, 19, 10.1016/0375-9601(95)00954-X
Gibbons, 1999, “Conformal maps and reductions of the Benney equations”, Physics Letters, A 258, 263, 10.1016/S0375-9601(99)00389-8
Gindikin, 1998, “On the automorphism group of the generalized conformal structure of a symmetric R-space”, Differential Geomeometry and Its Applications, 8, 21, 10.1016/S0926-2245(97)00015-6
Grant, 1993, “On self-dual gravity”, Physical Review, D 47, 2606
Harris, 1992, “Algebraic geometry: A first course”
Hoevenaars, 2005, “Second order reductions of the WDVV equations related to classical Lie algebras”, Letters in Mathematical Physics, 71, 83, 10.1007/s11005-004-6029-x
Ibragimov, Transformation Groups Applied to Mathematical Physics
Joyce, 2005, Lectures on Special Lagrangian Geometry
Krichever, 1994, “The τ-function of the universal Whitham hierarchy, matrix models and topological field theories”, Communications on Pure and Applied Mathematics, 47, 437, 10.1002/cpa.3160470403
Krichever, 2005, “Integrable structure of the Dirichlet boundary problem in multiply-connected domains”, Communications in Mathematical Physics, 259, 1, 10.1007/s00220-005-1387-5
Landsberg, 2001, “The projective geometry of Freudental's magic square”, Journal of Algebra, 239, 477, 10.1006/jabr.2000.8697
Landsberg, 2002, “Construction and classification of complex simple Lie algebras via projective geometry”, Selecta Mathematica, New Series, 8, 137, 10.1007/s00029-002-8103-5
Lychagin, 1993, “A classification of Monge-Amp.re equations”, Annales Scientifiques de l'École Normale Supérieure, 26, 281, 10.24033/asens.1673
Beffa, 2007, “On completely integrable geometric evolutions of curves of Lagrangian planes”, Proc. Roy. Soc. Edinburgh Sect. A, 137, 111, 10.1017/S0308210505000600
Mañas, 2002, “Reductions and hodograph solutions of the dispersionless KP hierarchy”, Journal of Physics, A 35, 401
Marshakov, 2002, “Integrable structure of the Dirichlet boundary problem in two dimensions”, Communications in Mathematical Physics, 227, 131, 10.1007/s002200200629
Mokhov, 1994, “Bianchi transformation between the real hyperbolic Monge-Ampére equation and the Born Infeld equation”, Letters in Mathematical Physics, 32, 121, 10.1007/BF00739421
Mokhov, 2001, Symplectic and Poisson Geometry on Loop Spaces of Smooth Manifolds and Integrable Equations
Mukai, “Simple Lie algebras and Legendre variety”
Ovsienko, 1993, “Lagrange Schwarzian derivative and symplectic Sturm theory”, Annales de la Faculté des Sciences de Toulouse, 2, 73, 10.5802/afst.758
Pavlov, 2003, “New integrable (2+1)-equations of hydrodynamic type”, Russian Mathematical Surveys, 58, 384, 10.1070/RM2003v058n02ABEH000620
Pavlov, 2004, “Classifying integrable Egoroff hydrodynamic chains”, Theoretical and Mathematical Physics, 138, 45, 10.1023/B:TAMP.0000010632.20218.62
Plebański, 1975, “Some solutions of complex Einstein equations”, Journal of Mathematical Physics, 16, 2395, 10.1063/1.522505
Plebański, 1996, “The Lagrangian for a self-dual gravitational field as a limit of the SDYM Lagrangian”, Physics Letters, A 212, 22, 10.1016/0375-9601(96)00025-4
Takasaki, 1995, “Integrable hierarchies and dispersionless limit”, Reviews in Mathematical Physics, 7, 743, 10.1142/S0129055X9500030X
Tsarev, 1985, “Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type”, Soviet Mathematics: Doklady, 31, 488
Tsarev, 1991, “The geometry of Hamiltonian systems of hydrodynamic type. The generalized hodograph method”, Izvestiya Mathematics of the USSR: Izvestiya 37, 397, 10.1070/IM1991v037n02ABEH002069
Wiegmann, 2000, “Conformal maps and integrable hierarchies”, Communications in Mathematical Physics, 213, 523, 10.1007/s002200000249
Zabolotskaya, 1969, “Quasi-plane waves in the nonlinear acoustics of confined beams”, Soviet Physics: Acoustics, 15, 35
Zabrodin, 2001, “The dispersionless limit of the Hirota equations in some problems of complex analysis”, Theoretical and Mathematical Physics, 129, 1511, 10.1023/A:1012883123413
Zakharov, 1994, “Dispersionless limit of integrable systems in 2 + 1dimensions”, Singular Limits of Dispersive Waves, 165, 10.1007/978-1-4615-2474-8_13
Zelenko, 2005, “Complete Systems of Invariants for Rank 1 Curves in Lagrange Grassmannians”, Differential Geometry and Its Applications, 367