Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 006, 13 pages      arXiv:1206.3751      http://dx.doi.org/10.3842/SIGMA.2013.006

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

Received October 01, 2012, in final form January 12, 2013; Published online January 20, 2013

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.

Key words: Novikov-Veselov equation; $N$-solitons solutions; Pfaffian expansion; wave functions.

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