Rogue waves, rational solutions, the patterns of their zeros and integral relations

Adrian Ankiewicz; Peter A. Clarkson; Nail Akhmediev

doi:10.1088/1751-8113/43/12/122002

Rogue waves, rational solutions, the patterns of their zeros and integral relations

Adrian Ankiewicz^*
, Peter A. Clarkson
, Nail Akhmediev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

127 Citations (Scopus)

Abstract

The focusing nonlinear Schrödinger equation, which describes generic nonlinear phenomena, including waves in the deep ocean and light pulses in optical fibres, supports a whole hierarchy of recently discovered rational solutions. We present recurrence relations for the hierarchy, the pattern of zeros for each solution and a set of integral relations which characterizes them.

Original language	English
Article number	122002
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	43
Issue number	12
DOIs	https://doi.org/10.1088/1751-8113/43/12/122002
Publication status	Published - 2010

Access to Document

10.1088/1751-8113/43/12/122002

Cite this

@article{372823ac7cf348a48ffd5ccfdcd1dd9e,

title = "Rogue waves, rational solutions, the patterns of their zeros and integral relations",

abstract = "The focusing nonlinear Schr{\"o}dinger equation, which describes generic nonlinear phenomena, including waves in the deep ocean and light pulses in optical fibres, supports a whole hierarchy of recently discovered rational solutions. We present recurrence relations for the hierarchy, the pattern of zeros for each solution and a set of integral relations which characterizes them.",

author = "Adrian Ankiewicz and Clarkson, \{Peter A.\} and Nail Akhmediev",

year = "2010",

doi = "10.1088/1751-8113/43/12/122002",

language = "English",

volume = "43",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "12",

}

TY - JOUR

T1 - Rogue waves, rational solutions, the patterns of their zeros and integral relations

AU - Ankiewicz, Adrian

AU - Clarkson, Peter A.

AU - Akhmediev, Nail

PY - 2010

Y1 - 2010

N2 - The focusing nonlinear Schrödinger equation, which describes generic nonlinear phenomena, including waves in the deep ocean and light pulses in optical fibres, supports a whole hierarchy of recently discovered rational solutions. We present recurrence relations for the hierarchy, the pattern of zeros for each solution and a set of integral relations which characterizes them.

AB - The focusing nonlinear Schrödinger equation, which describes generic nonlinear phenomena, including waves in the deep ocean and light pulses in optical fibres, supports a whole hierarchy of recently discovered rational solutions. We present recurrence relations for the hierarchy, the pattern of zeros for each solution and a set of integral relations which characterizes them.

UR - https://www.scopus.com/pages/publications/77949350470

U2 - 10.1088/1751-8113/43/12/122002

DO - 10.1088/1751-8113/43/12/122002

M3 - Article

SN - 1751-8113

VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 12

M1 - 122002

ER -

Rogue waves, rational solutions, the patterns of their zeros and integral relations

Abstract

Access to Document

Other files and links

Fingerprint

Cite this