Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-09-04
J.Phys. A. 44(2011) 305203(22pp)
Nonlinear Sciences
Exactly Solvable and Integrable Systems
21 papge, 10 figures
Scientific paper
10.1088/1751-8113/44/30/305203
The n-fold Darboux transformation (DT) is a 2\times2 matrix for the Kaup-Newell (KN) system. In this paper,each element of this matrix is expressed by a ratio of $(n+1)\times (n+1)$ determinant and $n\times n$ determinant of eigenfunctions. Using these formulae, the expressions of the $q^{[n]}$ and $r^{[n]}$ in KN system are generated by n-fold DT. Further, under the reduction condition, the rogue wave,rational traveling solution, dark soliton, bright soliton, breather solution, periodic solution of the derivative nonlinear Schr\"odinger(DNLS) equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions. The complete classification of these solutions generated by one-fold DT is given in the table on page.
He Jingsong
Wang Lihong
Xu Shuwei
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