This article is cited in 4 papers

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

Jen-Hsu Chang

Department of Computer Science and Information Engineering, National Defense University, Tauyuan, Taiwan

Abstract: 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.

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

MSC: 35C08; 35A22

Received: October 1, 2012; in final form January 12, 2013; Published online January 20, 2013

Language: English

DOI: 10.3842/SIGMA.2013.006

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ArXiv: 1206.3751