$N$-periodic wave solutions to the ${\cal N} =1$ supersymmetric Sawada-Kotera-Ramani equation

Abstract

Abstract The $N$-periodic wave solvability problem for the ${\cal N} =1$ supersymmetric Sawada-Kotera-Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the $N$-periodic wave solutions are derived. It has been verified that under some certain conditions, the asymptotic relations between $N$-periodic wave solutions and $N$-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.