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

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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. 
@article{TMF_1999_118_3_a11,
     author = {V. R. Kudashev and B. I. Suleimanov},
     title = {Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {413--422},
     publisher = {mathdoc},
     volume = {118},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a11/}
}
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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/