Relation between hyperbolic Nizhnik-Novikov-Veselov equation and stationary Davey-Stewartson II equation

Details Relation between hyperbolic Nizhnik-Novikov-Veselov equation and stationary Davey-Stewartson II equation Relation between hyperbolic Nizhnik-Novikov-Veselov equation and stationary Davey-Stewartson II equation

2008-10-27

arxiv.org/abs/0810.4767v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

25 pages, 5 figures

Scientific paper

10.1088/0266-5611/25/2/025003

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. Using Darboux transformation, global $n$-soliton solutions are obtained. It is proved that each $n$-soliton solution approaches zero uniformly and exponentially at spatial infinity and is asymptotic to $n^2$ lumps of peaks at temporal infinity.

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