质量等于孤立子质量的聚焦非线性系统爆破解的确定

IF 2.4 1区数学 Q1 MATHEMATICS Annals of Pde Pub Date : 2022-12-17 DOI:10.1007/s40818-022-00142-5

Benjamin Dodson

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引用次数: 7

摘要

在本文中，我们证明了质量等于孤立子质量的聚焦质量临界非线性Schrödinger方程在维数为（2，d，15）的爆破解的刚度。我们证明了唯一这样的解是孤立子和孤立子的伪共形变换。我们证明了这意味着非线性薛定谔方程的Liouville结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Determination of the Blowup Solutions to the Focusing NLS with Mass Equal to the Mass of the Soliton

In this paper we prove rigidity for blowup solutions to the focusing, mass-critical nonlinear Schrödinger equation in dimensions \(2 \le d \le 15\) with mass equal to the mass of the soliton. We prove that the only such solutions are the solitons and the pseudoconformal transformation of the solitons. We show that this implies a Liouville result for the nonlinear Schrödinger equation.

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