Geodesic
Reconstructions of the asymptotics of an integral determined by a hyperbolic unimodal singularity
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 60-74

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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.
Keywords: hyperbolic unimodal singularity, Laplace method, asymptotics, Whitney pleat, vector Burgers equation. 
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     author = {S. V. Zakharov},
     title = {Reconstructions of the asymptotics of an integral determined by a hyperbolic unimodal singularity},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
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     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a4/}
}
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S. V. Zakharov. Reconstructions of the asymptotics of an integral determined by a hyperbolic unimodal singularity. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 60-74. http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a4/