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This article is cited in 29 scientific papers (total in 30 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
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
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
Linking options:
https://www.mathnet.ru/eng/tmf6274https://doi.org/10.4213/tmf6274 https://www.mathnet.ru/eng/tmf/v157/i2/p188
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Abstract page: | 908 | Full-text PDF : | 327 | References: | 88 | First page: | 17 |
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