Revisit of rogue wave solutions in the Yajima–Oikawa system

The general rogue wave solutions for the one-dimensional (1D) Yajima–Oikawa (YO) system are derived through Hirota’s bilinear method and the Kadomtsev–Petviashvili hierarchy reduction method. Different from the previous work, we improve the construction of the differential operators to save the comp...

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Bibliographic Details
Published inNonlinear dynamics Vol. 111; no. 10; pp. 9439 - 9455
Main Authors He, Aolin, Huang, Peng, Zhang, Guangxiong, Huang, Jiaxing
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.05.2023
Springer Nature B.V
Subjects
Algebra
Automotive Engineering
Classical Mechanics
Control
Differential equations
Dynamical Systems
Engineering
Mathematical analysis
Mathematical functions
Mechanical Engineering
Memorial services
Operators (mathematics)
Original Paper
Polynomials
Vibration
Universal patterns
One-dimensional Yajima–Oikawa system
KP hierarchy
Rogue wave
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Summary:The general rogue wave solutions for the one-dimensional (1D) Yajima–Oikawa (YO) system are derived through Hirota’s bilinear method and the Kadomtsev–Petviashvili hierarchy reduction method. Different from the previous work, we improve the construction of the differential operators to save the complicated recursiveness and obtain the rogue wave solutions in a purely algebraic expression. Based on this simple expression, the new shape of the third-order rogue waves’ arrangement is found. Moreover, three types of fundamental rogue waves and the rogue wave patterns from second to fifth order are graphically illustrated. In particular, there exist N - 1 ( 2 ≤ N ) polygonal configurations of N th-order rogue waves for the 1D YO system, which is proven to be related to the Yablonskii–Vorob’ev polynomial hierarchy.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-023-08306-z