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Darboux transformation and Rogue waves of the Kundu–nonlinear Schrödinger equation
Author(s) -
Zhang Chengchuang,
Li Chuanzhong,
He Jingsong
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3232
Subject(s) - rogue wave , mathematics , breather , transformation (genetics) , eigenfunction , nonlinear schrödinger equation , nonlinear system , soliton , mathematical analysis , mathematical physics , order (exchange) , matrix (chemical analysis) , eigenvalues and eigenvectors , schrödinger equation , physics , quantum mechanics , biochemistry , chemistry , materials science , finance , economics , composite material , gene
In this paper, the Darboux transformation of the Kundu–nonlinear Schrödinger equation is derived and generalized to the matrix of n ‐fold Darboux transformation. From known solution Q , the determinant representation of n ‐th new solutions of Q [ n ] are obtained by the n ‐fold Darboux transformation. Then soliton solutions and positon solutions are generated from trivial seed solutions, breather solutions and rogue wave solutions that are obtained from periodic seed solutions. After that, the higher order rogue wave solutions of the Kundu–nonlinear Schrödinger equation are given. We show that free parameters in eigenfunctions can adjust the patterns of the higher order rogue waves. Meanwhile, the third‐order rogue waves are given explicitly. Copyright © 2014 John Wiley & Sons, Ltd.