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The Moutard transformation and its applications

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Discrete Integrable Systems

We discuss the Moutard transformation which is a two-dimensional generalization of the Darboux transformation of the Schroedinger operator and expose some applications of this transformations to spectral theory and soliton equations. In particular, we expose examples of Schroedinger operators with smooth fast-decaying potentials and nontrivial kernels in $L_2$ and of blowing up solutions of the Novikov—Veselov equation, a two-dimensional generalization of the Korteweg—de Vries equation. These results we obtained jointly with S.P. Tsarev.

This talk is part of the Isaac Newton Institute Seminar Series series.

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