Variable separation solutions obtained from Darboux transformations for the asymmetric Nizhnik-Novikov-Veselov system

The use of a seed-solution with some arbitrary functions for the asymmetric Nizhnik-Novikov-Veselov system in the first step Darboux, transformation yields the variable separable solutions with two space-variable separated functions. The more variable separated functions which are not arbitrary can be introduced by using the Darboux transformation repeatedly. The Nth step Darboux transformation (for arbitrary AT) with arbitrary number of space-variable separated functions is explicitly written down by means-of the Pfaffian. The universal variable separation formula which is valid for a diversity of. (2 + 1)-dimensional integrable systems can be obtained. from a particular reduction of the solutions constructed from the second step Darboux transformation. A new saddle-type, ring soliton solution with completely elastic interaction and nonzero phase shifts is also studied in this paper. (C) 2004 Elsevier Ltd. All rights reserved.