arXiv subjects
Publications and source records attributed to Eugene V. Ferapontov.
We investigate homogeneous third-order Hamiltonian operators of differential-geometric type. Based on the correspondence with quadratic line complexes, a complete list of such operators for two and three components is obtained.
Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system \[ \begin{split} &\partial ψ_{1} = (|ψ_{1}|^{2} + |ψ_{2}|^{2}) ψ_{2} \\ &\bar{\partial} ψ_{2} =- (|ψ_{1}|^{2} + |ψ_{2}|^{2}) ψ_{1} \end{split} \] descriptive of CMC surfaces within the framework of the generalized Weierstrass representation, decouples into a direct sum of the elliptic Sh-Gordon and Laplace equations. Connections of this system with the sigma model equations are established. It is pointed out, that the instanton solutions correspond to different Weierstrass parametrizations of the standard sphere $S^{2} \subset E^{3}$.