Higher-order semirational solutions and nonlinear wave interactions for a derivative nonlinear Schrodinger equation

作者：Wang, Lei^*; Zhu, Yu-Jie; Wang, Zi-Zhe; Qi, Feng-Hua; Guo, Rui

来源：Communications in Nonlinear Science & Numerical Simulation, 2016, 33: 218-228.

DOI：10.1016/j.cnsns.2015.08.027

• Derivative nonlinear Schrodinger equation
• Semirational solution
• Breather
• Rogue wave
• Nonlinear wave interaction
• Modified Darboux transformation

We present the semirational solution in terms of the determinant form for the derivative nonlinear Schrodinger equation. It describes the nonlinear combinations of breathers and rogue waves (RWs). We show here that the solution appears as a mixture of polynomials with exponential functions. The k-order semirational solution includes k - 1 types of nonlinear superpositions, i.e., the I-order RW and (k-l)-order breather for l = 1, 2,..., k - 1. By adjusting the shift and spectral parameters, we display various patterns of the semirational solutions for describing the interactions among the RWs and breathers. We find that k-order RW can be derived from a I-order RW interacting with 1/2(k - l)(k + l + 1) neighboring elements of a (k - l)-order breather for l = 1, 2,. . ., k - 1.

• 出版日期2016-4
• 单位太原理工大学; 北京物资学院