在实轴上具有二次非线性的高阶非线性Schrödinger方程

IF 1.5 3区数学 Q1 MATHEMATICS

Advances in Differential Equations Pub Date : 2022-03-28 DOI:10.57262/ade028-0506-413

A. Faminskii

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引用次数: 3

摘要

考虑了一类高阶非线性Schr方程的初值问题\具有二次非线性的奥丁格方程。得到了弱解的存在性和唯一性的结果。在无限大有效附加阻尼的情况下，还建立了不存在任何小假设的解的大时间衰减。研究的主要困难是非线性的非光滑性。

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The higher order nonlinear Schrödinger equation with quadratic nonlinearity on the real axis

The initial value problem is considered for a higher order nonlinear Schr\"odinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional damping large-time decay of solutions without any smallness assumptions is also established. The main difficulty of the study is the non-smooth character of the nonlinearity.

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来源期刊

Advances in Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.