The Nizhnik–Veselov–Novikov equation with self-consistent sources

Wang Hong-Yan<sup>abc

a</sup> Graduate University of the Chinese Academy of Sciences
^b Institute of Computational Mathematics and Scientific/Engineering Computing
^c School of Information, Renmin University of China

Abstract: We construct the coupled generalization of the Nizhnik–Veselov–Novikov (NVN) equation, i.e., the NVN equation with self-consistent sources (ESCS) and solve it using the so-called source generation procedure. We obtain BKP-type and DKP-type Pfaffian solutions of the NVN ESCS. In addition, we give a bilinear Bäcklund transformation and a Lax pair for the NVN ESCS. Furthermore, this Lax pair can be reduced to a Lax pair for the NVN equation.

Keywords: Nizhnik–Veselov–Novikov equation, self-consistent source, “source generation” procedure, Bäcklund transformation, Lax pair.

Received: 22.11.2007
Revised: 02.01.2008

DOI: 10.4213/tmf6268

 English version: Theoretical and Mathematical Physics, 2008, 157:1, 1474–1483

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