(2D) geometry. A time-dep endent conformal transformation maps a

fluid d omain into the lower complex half-plane of a new s patial

variable. The fluid dynamics is fully c haracterized by the complex

singularities in t he upper complex half-plane of the conformal map

(corresponds e.g. to oceanic wav es dynamics) and a dynamics of

superfluid Heli um 4 with two fluid components are considered. Bot h

systems share the same type of the non-canon ical Hamiltonian

structure. A superfluid Heliu m case is shown to be completely

integrable fo r the zero gravity and surface tension limit with the

exact reduction to the Laplace growth equa tion which is completely

integrable through th e connection to the dispersionless limit of the

integrable Toda hierarchy and existence of the i nfinite set of

complex pole solutions. A singl e fluid case with nonzero gravity and

surface tension turns more complicated with the infinite s et of new

moving poles solutions found which a re however unavoidably coupled

with the emergi ng moving branch points in the upper half-plane.

commute with each other in the sense of underlying non-canonical

Hamiltonian dynamics. It suggests that the existence of these extra

constants of motion provides an argumen t in support of the

conjecture of complete Ham iltonian integrability of 2D free surface

hydr odynamics.

LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR