Abstract:
The asymptotic behavior of an exponential integral is studied in which the phase function has the form
of a special deformation of the germ of a hyperbolic unimodal singularity of type $T_{4,4,4}$.
The integral under examination satisfies the heat equation, its Cole–Hopf transformation gives a solution
of the vector Burgers equation in four-dimensional space-time, and its principal asymptotic approximations
are expressed in terms of real solutions of systems of third-degree algebraic equations. The obtained
analytical results make it possible to trace the bifurcations of an asymptotic structure depending on the
parameter of the modulus of the singularity.
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