弱色散极限下具有大初始梯度的非线性薛定谔方程的考奇问题

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI:10.1134/s0040577924040019

S. V. Zakharov

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引用次数: 0

摘要

摘要我们考虑了具有大梯度初始函数和小分散参数的立方非线性薛定谔方程的 Cauchy 问题。利用重正化方法以积分卷积的显式形式构建渐近解。在由分散参数决定的缩放变换下，建立了重正化群性质的渐近类似物。在负聚焦系数的情况下，用已知的椭圆特殊函数得到了渐近解的清晰表达式。

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Cauchy problem for a nonlinear Schrödinger equation with a large initial gradient in the weakly dispersive limit

Abstract

We consider the Cauchy problem for the cubic nonlinear Schrödinger equation with a large gradient of the initial function and a small dispersion parameter. The renormalization method is used to construct an asymptotic solution in the explicit form of integral convolution. An asymptotic analogue of the renormalization group property is established under scaling transformations determined by the dispersion parameter. In the case of a negative focusing coefficient, a clarifying expression is obtained for the asymptotic solution in terms of known elliptic special functions.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.