Two-dimensional rational solitons and their blow-up via the Moutard transformation

Details Two-dimensional rational solitons and their blow-up via the Moutard transformation Two-dimensional rational solitons and their blow-up via the Moutard transformation

2008-01-21

arxiv.org/abs/0801.3225v2

Theoret. and Math. Phys. 157 (2007), 1525-1541

Physics

Mathematical Physics

22 pages, PDFLatex, 9 figures. v2: some computations corrected

Scientific paper

10.1007/s11232-008-0127-3

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 $L_2$-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

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