English

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 L2L_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

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