On the $N$-Solitons Solutions in the Novikov–Veselov Equation

We construct the $N$-solitons solution in the Novikov–Veselov equation from the extended Moutard transformation and the Pfaffian structure. Also, the corresponding wave functions are obtained explicitly. As a result, the property characterizing the $N$-solitons wave function is proved using the Pfaffian expansion. This property corresponding to the discrete scattering data for $N$-solitons solution is obtained in [arXiv:0912.2155] from the $\overline\partial$-dressing method.