%A ?. ?. ?????????? %J ??????? ????? ????????? ?????????? ??? ??????? %T ???????????????? ??????? ? ?????? ??????? ?????? ????????? ????????????? %X It is known that in some commutative associative algebras the exponential function is a solution of linear partial di?erential equations with constant coe?cients. In the present paper we propose a procedure allowing us to ?nd all components of the exponent in a special N-dimensional commutative algebra, where N is an arbitrary ?xed natural number. This allows us to construct solutions of one hydrodynamic equation of the third order %N 1 %P 262-274 %V 14 %D 2017 %I ??? ??????? %L zu226440