title: Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions.
abstract: In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger equation. The associated N-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the Nth-order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation. In particular, the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.
authors.affiliation: Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China.
authors.forename: Boling
authors.initials: B
authors.lastname: Guo
authors.forename: Liming
authors.initials: L
authors.lastname: Ling
authors.forename: Q P
authors.initials: QP
authors.lastname: Liu