The integrable KdV6 equations: Multiple soliton solutions and multiple singular soliton solutions

In this work, the completely integrable sixth-order nonlinear equations KdV6 are studied. Three distinct cases of these equations are selected for a reliable treatment. Multiple soliton solutions and multiple singular soliton solutions are formally derived for these equations. The Cole–Hopf transformation method combined with the Hirota’s bilinear sense are used to determine the two distinct structures of solutions. The resonance relations for the three cases are investigated.