Гиперкомплексные функции и точные решения одного уравнения гидродинамики

Abstract

It is known that in some commutative associative algebras the exponential function is a solution of linear partial differential equations with constant coefficients. In the present paper we propose a procedure allowing us to find all components of the exponent in a special N-dimensional commutative algebra, where N is an arbitrary fixed natural number. This allows us to construct solutions of one hydrodynamic equation of the third order.