## Abstract In this paper we consider the inverse scattering problem for the non‐linear Schrödinger equation on the line \def\dr{{\rm d}}$$i{\partial\over\partial t}u(t,x)=‐{\dr^2\over\dr x^2}u(t,x)+V\_0(x)u(t,x)+\sum\_{j=1}^{\infty}V\_j(x)|u|^{2(j\_0+j)}u(t,x)$$\nopagenumbers\end We prove, unde
Modified wave operators for the fourth-order non-linear Schrödinger-type equation with cubic non-linearity
✍ Scribed by Jun-ichi Segata
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 152 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.751
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✦ Synopsis
Abstract
We consider the scattering problem for the fourth‐order non‐linear Schrödinger‐type equation:
equation image
We show the existence of the modified wave operators for the above equation with cubic case by imposing the mean zero condition for the final data. Copyright © 2006 John Wiley & Sons, Ltd.
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