J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, A. S. Fokas
We introduce a mechanism for generating higher order rogue waves (HRWs) of the nonlinear Schr\"odinger(NLS) equation: the progressive fusion and fission of $n$ degenerate breathers associated with a critical eigenvalue $\lambda_0$, creates an order $n$ HRW. By adjusting the relative phase of the breathers at the interacting area it is possible to obtain different types of HRWs. The value $\lambda_0$ is a zero point of the eigenfunction of the Lax pair of the NLS equation and it corresponds to an infinitely large period of the breather. 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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http://arxiv.org/abs/1209.3742
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