A class of Hamiltonian deformations of plane curves is defined and studied. Hamiltonian deformations of conics and cubics are considered as illustrative examples. These deformations are described by systems of hydrodynamical-type equations. It is shown that solutions of these systems describe processes of formation of singularities (cusps, nodes), bubbles and change of the genus of a curve. © 2010 IOP Publishing Ltd.
Konopelchenko, B., Ortenzi, G. (2010). Hamiltonian motions of plane curves and formation of singularities and bubbles. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 43(19) [10.1088/1751-8113/43/19/195204].
Hamiltonian motions of plane curves and formation of singularities and bubbles
ORTENZI, GIOVANNIUltimo
2010
Abstract
A class of Hamiltonian deformations of plane curves is defined and studied. Hamiltonian deformations of conics and cubics are considered as illustrative examples. These deformations are described by systems of hydrodynamical-type equations. It is shown that solutions of these systems describe processes of formation of singularities (cusps, nodes), bubbles and change of the genus of a curve. © 2010 IOP Publishing Ltd.
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