M. Cerkaski, AN APPLICATION OF LAXS FORMALISM TO A CLASS OF CURVILINEAR AXIALLY-SYMMETRICAL COORDINATES IN 3-DIMENSIONAL SPACE, Journal of mathematical physics, 39(6), 1998, pp. 3236-3245
Solutions of a nonlinear system of differential partial equations in t
wo-dimensional space are studied. We prove that the considered system
is fully integrable and that its solutions determine an infinite class
of mappings of the space of curvilinear axially symmetric coordinates
onto the space of cylindric coordinates, The corresponding family of
reverse transformations is found in a closed form. An infinite number
of the first integrals of the nonlinear system is obtained. Symmetries
of a class of electrostatic systems associated with the considered fa
mily of curvilinear coordinates are discussed. (C) 1998 American Insti
tute of Physics.