三维三次五次NLS的阈值解

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2022-08-17 DOI:10.1080/03605302.2023.2212477

Alex H. Ardila, Jason Murphy

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引用次数: 3

摘要

摘要我们研究了三维空间中的三次五次非线性系统。众所周知，散射适用于在对应于正维里的区域中具有质量能量的解，其边界由基态孤子及其某些重新缩放来划定。我们对仅由孤子获得的边界部分的解的可能行为进行了分类。特别地，我们证明了非孤立子解要么在两个时间方向上散射，要么与一个特殊解重合（模对称性），该特殊解在一个时间方向散射，并指数收敛于另一个方向的孤立子。

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Threshold solutions for the 3d cubic-quintic NLS

Abstract We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundary of which is delineated both by ground state solitons and by certain rescalings thereof. We classify the possible behaviors of solutions on the part of the boundary attained solely by solitons. In particular, we show that non-soliton solutions either scatter in both time directions or coincide (modulo symmetries) with a special solution, which scatters in one time direction and converges exponentially to the soliton in the other.

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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.