On the relation between the dual AKP equation and an equation by King and Schief, and its N-soliton solution

Abstract: The dual of the lattice AKP equation [P.H. van der Kamp et al., J. Phys. A 51, 365202 (2018)] is equivalent to a 14-point equation related to the lattice BKP equation, found by King and Schief. If one of the parameters vanishes, it is equivalent to a 12-point equation related to the lattice AKP equation. This establishes the integrability of the dual AKP equation. Using the equivalence we prove the existence of the conjectured $N$-soliton solution of the dual AKP equation, for all values of the parameters.