Abstract
The general solution of the system of differential equations describing Egorov hydrodynamic chains is constructed. The solution is given in terms of the elliptic sigma function. Invariants of the sigma function are expressed as differential polynomials in a solution of the Chazy equation. The orbits of the induced action of SL(2,ℂ) and degenerating operators in the space of solutions are described.
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Buchstaber, V.M., Leykin, D.V. & Pavlov, M.V. Egorov Hydrodynamic Chains, the Chazy Equation, and SL(2,ℂ). Functional Analysis and Its Applications 37, 251–262 (2003). https://doi.org/10.1023/B:FAIA.0000015576.05085.bc
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DOI: https://doi.org/10.1023/B:FAIA.0000015576.05085.bc