Two-dimensional rational solitons and their blowup via the moutard transformation
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- Taimanov, I.A. & Tsarev, S.P. Theor Math Phys (2008) 157: 1525. doi:10.1007/s11232-008-0127-3
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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.