Source generation of the Davey-Stewartson equation

Abstract

The “source generation” procedure (SGP) proposed by Hu and Wang [Inverse Probl. 22, 1903 (2006)] provides a new way to systematically generate so-called soliton equations with self-consistent sources. In this paper, we apply this SGP to a Davey-Stewartson (DS) equation based on the Hirota bilinear form, producing a system of equations which is called the DS equation with self-consistent sources (DSESCS). Meanwhile, we obtain the Gramm-type determinant solutions to the DSESCS. Since the DS equation is a (2+1)-dimensional integrable generalization of the nonlinear Schrödinger (NLS) equation, the DSESCS may be viewed as a (2+1)-dimensional integrable generalization of the nonlinear Schrödinger equation with self-consistent sources. These results indicate the commutativity of source generation procedure and (2+1)-dimensional integrable generalizations for the NLS equation.