, Volume 157, Issue 2, pp 1525-1541
Date: 04 Dec 2008

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

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Abstract

We construct a family of two-dimensional stationary Schrödinger operators with rapidly decaying smooth rational potentials and nontrivial L2 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 ≥ t0 > 0.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 188–207, November, 2008.