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arXiv · 1809.04225

On the dispersionless Davey-Stewartson system: Hamiltonian vector fields Lax pair and relevant nonlinear Riemann-Hilbert problem for dDS-II system

G. Yi
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Abstract

In this paper, the semiclassical limit of Davey-Stewartson systems are studied. It shows that these dispersionless limited integrable systems of hydrodynamic type, which are defined as dDS (dispersionless Davey-Stewartson) systems, are arisen from the commutation condition of Lax pairs of one-parameter vector fields. The relevant nonlinear Riemann-Hilbert problems with some symmetries for the dDS-II system are also constructed. This kind of Riemann-Hilbert problems are meaningful for applying the formal inverse scattering transform method, recently developed by Manakov and Santini, to study the dDS-II system .

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G. Yi. 2019-05-01. On the dispersionless Davey-Stewartson system: Hamiltonian vector fields Lax pair and relevant nonlinear Riemann-Hilbert problem for dDS-II system. https://doi.org/10.1007/s11005-019-01224-5

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