MG11 
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Thirty years of studies of integrable reductions of Einstein's field equations (opening remarks)

In this talk, after some historical remarks, we recall the key-points of Belinski - Zakharov inverse scattering approach and soliton technique for vacuum Einstein equations (1978) and the author's modification of this approach for Einstein - Maxwell fields (1980). Then we describe the integrability structure in spacetimes of any dimensions D>=4 of the symmetry reduced low-energy dynamics of the bosonic sector of heterotic string effective action. For these equations which govern gravitational, dilaton, antisymmetric tensor and any number n of Abelian vector gauge fields, we construct an equivalent (2 d+n)x(2 d+n)-matrix spectral problem (d=D-2), describe different types of soliton generating transformations and outline the monodromy transform approach and linear singular integral equation methods for their solution.

Einstein's field equations in the context of theory of integrable systems: from vacuum solitons to integrable field dynamics in string gravity theories

In this talk, after some historical remarks, we recall the key-points of Belinski - Zakharov inverse scattering approach and soliton technique for vacuum Einstein equations (1978) and the author's modification of this approach for Einstein - Maxwell fields (1980). Then we describe the integrability structure in spacetimes of any dimensions D>=4 of the symmetry reduced low-energy dynamics of the bosonic sector of heterotic string effective action. For these equations which govern gravitational, dilaton, antisymmetric tensor and any number n of Abelian vector gauge fields, we construct an equivalent (2 d+n)x(2 d+n)-matrix spectral problem (d=D-2), describe different types of soliton generating transformations and outline the monodromy transform approach and linear singular integral equation methods for their solution.