Geodesic
Two-dimensional rational solitons and their blowup via the~Moutard
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 188-207

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We construct a family of two-dimensional stationary Schrödinger operators with rapidly decaying smooth rational potentials and nontrivial $L_2$ kernels. We show that some of the constructed potentials generate solutions of the Veselov–Novikov equation that decay rapidly at infinity, are nonsingular at $t=0$, and have singularities at finite times $t\ge t_0>0$.
Keywords: two-dimensional Schrödinger operator, Veselov–Novikov equation, solution blowup.
Mots-clés : Moutard transformation 
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     author = {I. A. Taimanov and S. P. Tsarev},
     title = {Two-dimensional rational solitons and their blowup via {the~Moutard}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {188--207},
     publisher = {mathdoc},
     volume = {157},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a2/}
}
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I. A. Taimanov; S. P. Tsarev. Two-dimensional rational solitons and their blowup via the~Moutard. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 188-207. http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a2/