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arXiv · 0810.4767

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

Zi-Xiang Zhou
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Abstract

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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Zi-Xiang Zhou. 2008-10-27. Relation between hyperbolic Nizhnik-Novikov-Veselov equation and stationary Davey-Stewartson II equation. https://doi.org/10.1088/0266-5611%2F25%2F2%2F025003

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