Systems of Differential Equations for Determining the Fundamental Vector of Special Wave Catastrophes

Uniform asymptotic solutions of the field structures in the vicinity of focusing based on the use of the Maslov canonical operator leads to investigation of special functions of wave catastrophe (SWC) and their first derivatives. The method for constructing a system of differential equations to determine the fundamental vector of special functions of wave catastrophes (SWC) is created. This approach allows us to reduce the solution of the problem of determining the SWCs and their derivatives to the solution of the Cauchy problem for a system of ordinary differential equations. The paper provides examples of the construction of such systems for special functions of edge catastrophes corresponding to Lagrange manifolds with boundary and special functions of main catastrophes corresponding to Lagrange manifolds without restrictions.

DOI 10.1134/S1061920824040083