Soliton, breather and rogue wave solutions of the coupled Gerdjikov–Ivanov equation via Darboux transformation

The coupled Gerdjikov–Ivanov (cGI) equation, associated with a 3 × 3 matrix Lax pair, is an important integrable system that can be reduced to the third kind of derivative nonlinear Schrödinger equation, i.e., Gerdjikov–Ivanov equation. Based on the symmetric relations of the Lax pair, 2 N -fold Dar...

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Bibliographic Details
Published in:Nonlinear dynamics 2020-07, Vol.101 (1), p.619-631
Main Authors: Ji, Ting, Zhai, Yunyun
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Exact solutions
Mechanical Engineering
Original Paper
Schrodinger equation
Solitary waves
Transformations (mathematics)
Vibration
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Summary:The coupled Gerdjikov–Ivanov (cGI) equation, associated with a 3 × 3 matrix Lax pair, is an important integrable system that can be reduced to the third kind of derivative nonlinear Schrödinger equation, i.e., Gerdjikov–Ivanov equation. Based on the symmetric relations of the Lax pair, 2 N -fold Darboux transformation for the cGI equation is constructed. As an application of the Darboux transformation, we obtain some exact solutions of the cGI equation, including bright–bright soliton, dark–bright soliton, Ma breather, breather fission, soliton fusion and dark–bright rogue wave.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-05790-5