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

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. (C) 2015 Elsevier B.V. All rights reserved.