N-periodic wave solutions of the N=2 supersymmetric KdV equation

In this paper, the $N$-periodic wave solutions of the $N=2$ supersymmetric KdV equation are studied by combining the super Hirota bilinear form with the super Riemann-theta function, which can be used to describe new phenomena on super quasi-periodic waves with the fermionic field. With the aid of the Gauss–Newton method, the three-periodic and four-periodic wave solutions are obtained. In particular, these quasi-periodic waves can produce parallel, crossed and degenerated patterns. The analytical method related to the characteristic lines is used to analyze the dynamic characteristics of the three-periodic and four-periodic waves. In addition, it has been indicated that $N$-periodic waves can exist in the supersymmetric integrable systems.