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arXiv · 0801.3225

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

I. A. Taimanov·S. P. Tsarev
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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 $L_2$-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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I. A. Taimanov, S. P. Tsarev. 2008-02-11. Two-dimensional rational solitons and their blow-up via the Moutard transformation. https://doi.org/10.1007/s11232-008-0127-3

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