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

Jen-Hsu Chang

Symmetry, integrability and geometry: methods and applications, Tome 9 (2013)

Résumé

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.

Détail

Keywords: Novikov–Veselov equation; $N$-solitons solutions; Pfaffian expansion; wave functions.

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