AN APPLICATION OF LAXS FORMALISM TO A CLASS OF CURVILINEAR AXIALLY-SYMMETRICAL COORDINATES IN 3-DIMENSIONAL SPACE

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.