Blow-Up Criteria for the 1D NLS With Combined Nonlinearities

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2026-08-07 DOI:10.1111/sapm.70272

Alex D. Rodriguez

引用次数: 0

Abstract

In this paper, we develop two different types of criteria for the finite time blow-up solutions to the combined nonlinear Schrödinger equation in 1D. The first one is a negative energy criterion developed for triple combined nonlinearity and then for a (convergent) infinite sum of combined nonlinearities, including an exponential nonlinearity. The second one is a positive energy criterion for the double nonlinearity with the defocusing–focusing coefficients. We also provide examples of initial data that satisfy either of the criteria.

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组合非线性一维NLS的爆破判据

本文给出了一维组合非线性Schrödinger方程有限时间爆破解的两种判据。第一个是针对三重组合非线性的负能量判据，然后是针对（收敛的）无限组合非线性，包括指数非线性的负能量判据。第二种是带离焦-聚焦系数的双非线性的正能量判据。我们还提供了满足任何一个标准的初始数据的示例。

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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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.