### Abstract

Exact explicit rational solutions of two- and one-dimensional multicomponent Yajima-Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional system, the fundamental rational solution first describes the localized lumps, which have three different patterns: bright, intermediate and dark states. Then, rogue waves can be obtained under certain parameter conditions and their behaviors are also classified to above three patterns with different definition. It is shown that the simplest (fundamental) rogue waves are line localized waves which arise from the constant background with a line profile and then disappear into the constant background again. In particular, two-dimensional intermediate and dark counterparts of rogue wave are found with the different parameter requirements. We demonstrate that multirogue waves describe the interaction of several fundamental rogue waves, in which interesting curvy wave patterns appear in the intermediate times. Different curvy wave patterns form in the interaction of different types fundamental rogue waves. Higher-order rogue waves exhibit the dynamic behaviors that the wave structures start from lump and then retreat back to it, and this transient wave possesses the patterns such as parabolas. Furthermore, different states of higher-order rogue wave result in completely distinguishing lumps and parabolas. Moreover, one-dimensional rogue wave solutions with three states are constructed through the further reduction. Specifically, higher-order rogue wave in one-dimensional case is derived under the parameter constraints.

Original language | English |
---|---|

Pages (from-to) | 1510-1519 |

Number of pages | 10 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 379 |

Issue number | 24-25 |

DOIs | |

Publication status | Published - 2015 Jul 31 |

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### Keywords

- Bilinear method
- Multicomponent
- Rational solution
- Two-dimensional dark rogue wave
- Yajima-Oikawa system

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*379*(24-25), 1510-1519. https://doi.org/10.1016/j.physleta.2015.02.040

**Rational solutions to two- and one-dimensional multicomponent Yajima-Oikawa systems.** / Chen, Junchao; Chen, Yong; Feng, Bao Feng; Maruno, Kenichi.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 379, no. 24-25, pp. 1510-1519. https://doi.org/10.1016/j.physleta.2015.02.040

}

TY - JOUR

T1 - Rational solutions to two- and one-dimensional multicomponent Yajima-Oikawa systems

AU - Chen, Junchao

AU - Chen, Yong

AU - Feng, Bao Feng

AU - Maruno, Kenichi

PY - 2015/7/31

Y1 - 2015/7/31

N2 - Exact explicit rational solutions of two- and one-dimensional multicomponent Yajima-Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional system, the fundamental rational solution first describes the localized lumps, which have three different patterns: bright, intermediate and dark states. Then, rogue waves can be obtained under certain parameter conditions and their behaviors are also classified to above three patterns with different definition. It is shown that the simplest (fundamental) rogue waves are line localized waves which arise from the constant background with a line profile and then disappear into the constant background again. In particular, two-dimensional intermediate and dark counterparts of rogue wave are found with the different parameter requirements. We demonstrate that multirogue waves describe the interaction of several fundamental rogue waves, in which interesting curvy wave patterns appear in the intermediate times. Different curvy wave patterns form in the interaction of different types fundamental rogue waves. Higher-order rogue waves exhibit the dynamic behaviors that the wave structures start from lump and then retreat back to it, and this transient wave possesses the patterns such as parabolas. Furthermore, different states of higher-order rogue wave result in completely distinguishing lumps and parabolas. Moreover, one-dimensional rogue wave solutions with three states are constructed through the further reduction. Specifically, higher-order rogue wave in one-dimensional case is derived under the parameter constraints.

AB - Exact explicit rational solutions of two- and one-dimensional multicomponent Yajima-Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional system, the fundamental rational solution first describes the localized lumps, which have three different patterns: bright, intermediate and dark states. Then, rogue waves can be obtained under certain parameter conditions and their behaviors are also classified to above three patterns with different definition. It is shown that the simplest (fundamental) rogue waves are line localized waves which arise from the constant background with a line profile and then disappear into the constant background again. In particular, two-dimensional intermediate and dark counterparts of rogue wave are found with the different parameter requirements. We demonstrate that multirogue waves describe the interaction of several fundamental rogue waves, in which interesting curvy wave patterns appear in the intermediate times. Different curvy wave patterns form in the interaction of different types fundamental rogue waves. Higher-order rogue waves exhibit the dynamic behaviors that the wave structures start from lump and then retreat back to it, and this transient wave possesses the patterns such as parabolas. Furthermore, different states of higher-order rogue wave result in completely distinguishing lumps and parabolas. Moreover, one-dimensional rogue wave solutions with three states are constructed through the further reduction. Specifically, higher-order rogue wave in one-dimensional case is derived under the parameter constraints.

KW - Bilinear method

KW - Multicomponent

KW - Rational solution

KW - Two-dimensional dark rogue wave

KW - Yajima-Oikawa system

UR - http://www.scopus.com/inward/record.url?scp=84937762382&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937762382&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2015.02.040

DO - 10.1016/j.physleta.2015.02.040

M3 - Article

VL - 379

SP - 1510

EP - 1519

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 24-25

ER -