### Abstract

Rogue wave solutions up to the fifth-order are obtained by solving the modified nonlinear Schrödinger equation, also known as the Dysthe equation which provides a better representation of the wave evolution in space. Using the fourth-order split-step pseudo-spectral method during the integral process, more accurate results with a smaller conservation error were obtained. One of the key features is the adoption of the wavelet analysis method to analyse the time-frequency energy distribution during the generation and evolution of the hierarchy of so-called super rogue waves. It is revealed that a strong energy density surges instantaneously and is seemingly carried over to the high frequency components at the instant when a large, rogue wave occurs. Super rogue waves tend to be the consequence of the nonlinear superposition and focusing of waves in the time and space domain, where transient energy moves between the fundamental frequency and sideband frequencies.

Language | English |
---|---|

Pages | 295-307 |

Number of pages | 13 |

Journal | Ocean Engineering |

Volume | 113 |

Early online date | 22 Jan 2016 |

DOIs | |

Publication status | Published - 1 Feb 2016 |

### Fingerprint

### Keywords

- mNLS
- nonlinear Schrödinger equation
- rational solution
- super rogue wave

### Cite this

*Ocean Engineering*,

*113*, 295-307. https://doi.org/10.1016/j.oceaneng.2015.11.006

}

*Ocean Engineering*, vol. 113, pp. 295-307. https://doi.org/10.1016/j.oceaneng.2015.11.006

**Numerical study of the energy structure of super rogue waves.** / Lu, Wenyue; Yang, Jianmin; Tao, Longbin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical study of the energy structure of super rogue waves

AU - Lu, Wenyue

AU - Yang, Jianmin

AU - Tao, Longbin

PY - 2016/2/1

Y1 - 2016/2/1

N2 - Rogue wave solutions up to the fifth-order are obtained by solving the modified nonlinear Schrödinger equation, also known as the Dysthe equation which provides a better representation of the wave evolution in space. Using the fourth-order split-step pseudo-spectral method during the integral process, more accurate results with a smaller conservation error were obtained. One of the key features is the adoption of the wavelet analysis method to analyse the time-frequency energy distribution during the generation and evolution of the hierarchy of so-called super rogue waves. It is revealed that a strong energy density surges instantaneously and is seemingly carried over to the high frequency components at the instant when a large, rogue wave occurs. Super rogue waves tend to be the consequence of the nonlinear superposition and focusing of waves in the time and space domain, where transient energy moves between the fundamental frequency and sideband frequencies.

AB - Rogue wave solutions up to the fifth-order are obtained by solving the modified nonlinear Schrödinger equation, also known as the Dysthe equation which provides a better representation of the wave evolution in space. Using the fourth-order split-step pseudo-spectral method during the integral process, more accurate results with a smaller conservation error were obtained. One of the key features is the adoption of the wavelet analysis method to analyse the time-frequency energy distribution during the generation and evolution of the hierarchy of so-called super rogue waves. It is revealed that a strong energy density surges instantaneously and is seemingly carried over to the high frequency components at the instant when a large, rogue wave occurs. Super rogue waves tend to be the consequence of the nonlinear superposition and focusing of waves in the time and space domain, where transient energy moves between the fundamental frequency and sideband frequencies.

KW - mNLS

KW - nonlinear Schrödinger equation

KW - rational solution

KW - super rogue wave

UR - http://www.scopus.com/inward/record.url?scp=84955440871&partnerID=8YFLogxK

U2 - 10.1016/j.oceaneng.2015.11.006

DO - 10.1016/j.oceaneng.2015.11.006

M3 - Article

VL - 113

SP - 295

EP - 307

JO - Ocean Engineering

T2 - Ocean Engineering

JF - Ocean Engineering

SN - 0029-8018

ER -