Two-dimensional rational solitons and their blow-up via the Moutard transformation
Mathematical Physics
2009-11-13 v2 math.MP
Abstract
By using the Moutard transformation of two-dimensional Schroedinger operators we derive a procedure for constructing explicit examples of such operators with rational fast decaying potentials and degenerate -kernels (this construction was sketched in arXiv:0706.3595) and show that if we take some of these potentials as the Cauchy data for the Novikov-Veselov equation (a two-dimensional version of the Korteweg-de Vries equation), then the corresponding solutions blow up in a finite time
Keywords
Cite
@article{arxiv.0801.3225,
title = {Two-dimensional rational solitons and their blow-up via the Moutard transformation},
author = {I. A. Taimanov and S. P. Tsarev},
journal= {arXiv preprint arXiv:0801.3225},
year = {2009}
}
Comments
22 pages, PDFLatex, 9 figures. v2: some computations corrected