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

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.