### ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT

#### Abstract

We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.

#### Keywords

Matched asymptotic expansions, Numerical integration, Butterfly catastrophe, Nonlinear ODE

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