Geodesic
Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 413-422 
V. R. Kudashev; B. I. Suleimanov. Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 413-422. http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a11/
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     title = {Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation},
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Analogues of the Pearcey integral describe the small dispersion influence on the beginning of spontaneous-vanishing processes for the nonlinear geometric optic approximation amplitude, which is a solution of equations of the focusing nonlinear Schrödinger equation type. The asymptotic behavior as $x^2+t^2\to\infty$ of these analogues is considered. For $x^2+t^2\to\infty$, the special functions under consideration have a domain of small-amplitude high-frequency oscillations, which occur on the background of the nonzero-amplitude nonlinear geometric optic approximation.

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