A Lax system in three variables is presented, two equations of which form the Lax pair of the stationary Davey-Stewartson II equation. With certain nonlinear constraints, the full integrability condition of this Lax system contains the hyperbolic Nizhnik-Novikov-Veselov equation and its standard Lax pair. The Darboux transformation for the Davey-Stewartson II equation is used to solve the hyperbolic Nizhnik-Novikov-Veselov equation and global multi-soliton solutions are obtained. It is proved that the nxn soliton solution derived by the Darboux transformation of order n approaches zero uniformly and exponentially at spatial infinity and is asymptotic to n2 solitons at temporal infinity.
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