N-soliton solutions for the integrable bidirectional sixth-order Sawada–Kotera equation

In this work, the integrable bidirectional sixth-order Sawada–Kotera equation is examined. The equation considered is a KdV6 equation that was derived from the fifth order Sawada–Kotera equation. Multiple soliton solutions and multiple singular soliton solutions are formally derived for this equation. The Cole–Hopf transformation method combined with the Hirota’s bilinear method are used to determine the two sets of solutions, where each set has a distinct structure.