Abstract

In this work, general higher-order freak wave solutions of the focusing Kundu-Eckhaus equation can be calculated theoretically through a Darboux transformation by a separation of variable method. Moreover, the dynamics of first-order and second-order freak wave solutions are discussed with some graphics. In particular, we observe that one four-petaled freak wave and three eye-shaped ones can coexist, in contrast to the four eye-shaped ones reported before. They demonstrate that the structure of freak waves in this paper is richer than that in the well-known NLS equation.