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

[摘要] 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.

[关键词] Novikov–Veselov equation;N-solitons solutions;Pfaf fian expansion;wave functions