发表机构
Florida International University; Universidad Nacional de Colombia（佛罗里达国际大学; 哥伦比亚国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了低维（1、2、3维）四阶双调和非线性薛定谔方程在加权Sobolev子集及H^s空间中的局部适定性，为光学中四次孤子的数学理论奠定基础。
AI 中文摘要
本文研究维度1、2和3中的四阶（或双调和）非线性薛定谔（NLS）方程，其中势项表示为幂非线性（对于任何正幂），色散算子具有四阶与较低的二阶相结合。四阶NLS方程最近引起了研究者的关注，因为四次孤子已在光学中实验获得，因此，在物理维度N=1,2,3中发展四阶NLS方程解的数学理论是及时的。在这项工作中，我们证明了四阶或双调和NLS方程在Sobolev空间的加权子集以及H^s空间中的局部适定性。
英文摘要
In this paper we consider the 4th order (or biharmonic) nonlinear Schrödinger (NLS) equation in dimensions 1, 2, and 3, where the potential term is expressed as a power non-linearity (for any positive power) and the dispersion operator has the {\it fourth} order combined with the lower {\it second} order. The fourth order NLS equation has recently attracted attention of researchers since quartic solitons have been experimentally obtained in optics, and thus, mathematical theory of solutions to the 4th order NLS equation in physical dimensions $N=1,2,3$ is timely to develop. In this work we show the local well-posedness of the 4th order or bi-harmonic NLS equation on a weighted subset of a Sobolev space as well as in $H^s$ spaces.
Comments25 pages; appeared in Studies in Applied Mathematics
