title: Generating mechanism for higher-order rogue waves.
abstract: We introduce a mechanism for generating higher-order rogue waves (HRWs) of the nonlinear Schrödinger (NLS) equation: the progressive fusion and fission of n degenerate breathers associated with a critical eigenvalue λ(0) creates an order-n HRW. By adjusting the relative phase of the breathers in the interacting area, it is possible to obtain different types of HRWs. The value λ(0) is a zero point of an eigenfunction of the Lax pair of the NLS equation and it corresponds to the limit of the period of the breather tending to infinity. By employing this mechanism we prove two conjectures regarding the total number of peaks, as well as a decomposition rule in the circular pattern of an order-n HRW.
authors.affiliation: Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China. hejingsong@nbu.edu.cn
authors.forename: J S
authors.initials: JS
authors.lastname: He
authors.forename: H R
authors.initials: HR
authors.lastname: Zhang
authors.forename: L H
authors.initials: LH
authors.lastname: Wang
authors.forename: K
authors.initials: K
authors.lastname: Porsezian
authors.forename: A S
authors.initials: AS
authors.lastname: Fokas
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*