## Quasiclassical scattering of wave packets on a narrow band in which the potential rapidly changes.(English. Russian original)Zbl 0689.35080

Math. Notes 45, No. 1-2, 72-77 (1989); translation from Mat. Zametki 45, No. 1, 106-114 (1989).
Let $$\psi$$ satisfy an equation $i\hslash \partial \psi /\partial t=- \hslash^ 2\Delta \psi +| \nabla \Phi |^ 2V(\Phi (x)/\hslash)\psi +V_ 0(x)\psi,x\in {\mathbb{R}},$ and an initial condition $H_{t=0}=\phi_ 0(x) \exp (i\hslash^{-1}S(x)),$ where functions $$\phi_ 0,S_ 0,\Phi,V_ 0$$ and V are given. The asymptotics of $$\psi$$ (x,t,$$\hslash)$$ as $$\hslash \to 0$$ and $$t\in [0,T]$$ with fixed T is found.
Reviewer: D.R.Yafaev

### MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 35B40 Asymptotic behavior of solutions to PDEs 35K15 Initial value problems for second-order parabolic equations 35P25 Scattering theory for PDEs

### Keywords:

classical limit; nonlinear Schrödinger equation
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### References:

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