On completeness of the Moutard transformations

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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6 pages (17 Kbytes), standard LaTeX 2.09, run twice to get the right cross-references. Resubmitted with the only correction: a

Scientific paper

In this paper we solve positively the problem of (local) density of the
"potentials" M(x,y) of the Moutard equation, u_{xy} = M(x,y) u, u=u(x,y), (used
in many papers for construction of exact solutions of (2+1)-dimensional
integrable systems) obtainable from a given initial potential with consecutive
Moutard transformations.

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