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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 157, Number 2, Pages 188–207
DOI: https://doi.org/10.4213/tmf6274 (Mi tmf6274) 		 
This article is cited in 30 scientific papers (total in 31 papers)

Two-dimensional rational solitons and their blowup via the Moutard transformation

I. A. Taimanova, S. P. Tsarevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Krasnoyarsk State Pedagogical University named after V. P. Astaf'ev
Full-text PDF (1590 kB) Citations (31)
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DOI: https://doi.org/10.4213/tmf6274
Abstract: 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, Moutard transformation, Veselov–Novikov equation, solution blowup.
Received: 21.01.2008
English version:
Theoretical and Mathematical Physics, 2008, Volume 157, Issue 2, Pages 1525–1541
DOI: https://doi.org/10.1007/s11232-008-0127-3
Bibliographic databases:
Language: Russian
Citation: I. A. Taimanov, S. P. Tsarev, “Two-dimensional rational solitons and their blowup via the Moutard transformation”, TMF, 157:2 (2008), 188–207; Theoret. and Math. Phys., 157:2 (2008), 1525–1541
Citation in format AMSBIB
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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