## 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.

Original language | English |
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Article number | 013506 |

Journal | Journal of Mathematical Physics |

Volume | 49 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2008 |

## Scopus Subject Areas

- Statistical and Nonlinear Physics
- Mathematical Physics