Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side

Abstract

In the present paper, we use the theory of functions of noncommuting operators, also known as noncommutative analysis (which can be viewed as a far-reaching generalization of pseudodifferential operator calculus), to solve an asymptotic problem for a partial differential equation and show how, starting from general constructions and operator formulas that seem to be rather abstract from the viewpoint of differential equations, one can end up with very specific, easy-to-evaluate expressions for the solution, useful, e.g., in the tsunami wave problem.