Generating mechanism for higher-order rogue waves

Generating mechanism for higher-order rogue waves

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...

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Veröffentlicht in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2013-05, Vol.87 (5), p.052914-052914, Article 052914
Hauptverfasser: He, J S, Zhang, H R, Wang, L H, Porsezian, K, Fokas, A S
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Computer Simulation
Models, Theoretical
Nonlinear Dynamics
Oscillometry - methods
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container_title Physical review. E, Statistical, nonlinear, and soft matter physics
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creator He, J S
Zhang, H R
Wang, L H
Porsezian, K
Fokas, A S
description 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.
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Nonlinear Dynamics
Oscillometry - methods
title Generating mechanism for higher-order rogue waves
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