Rational and semi-rational solutions to the Davey–Stewartson III equation

In this paper, based on the combination of Hirota’s bilinear method and long wave limit technique, we investigate rational and semi-rational solutions to the third-type Davey–Stewartson (DS III) equation and its nonlocal version. Rational solutions to the DS III equation demonstrate to be kinks, lum...

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Bibliographic Details
Published in:Nonlinear dynamics 2023-04, Vol.111 (8), p.7635-7655
Main Authors: Wang, Sheng-Nan, Yu, Guo-Fu
Format: Article
Language:English
Subjects:
Automotive Engineering
Breathers
Classical Mechanics
Control
Dynamical Systems
Engineering
Mechanical Engineering
Optics
Original Paper
Photonics
Solitary waves
Symmetry
Vibration
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Summary:In this paper, based on the combination of Hirota’s bilinear method and long wave limit technique, we investigate rational and semi-rational solutions to the third-type Davey–Stewartson (DS III) equation and its nonlocal version. Rational solutions to the DS III equation demonstrate to be kinks, lumps and line rogue waves, while semi-rational solutions display hybrids of solitons, lumps and line rogue waves. As to the nonlocal DS III equation, we derive (semi-)rational solutions and breather solutions. Semi-rational solutions show lumps on the periodic line backgrounds, hybrids of breathers and lumps, line rogue waves and line breathers on the periodic line background.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-022-08219-3