Convective Modulation Instability of the Radiation of the Periodic Component in the Case of Resonance of Long and Short Waves

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-09-01 DOI:10.1134/s0081543823040107

引用次数: 0

Abstract

The main result of the paper is a theorem stating that the modulation instability of a carrier periodic wave of small (but finite) amplitude propagating in an arbitrary dispersive medium may only be convective in a reference frame moving at a velocity that differs finitely from the group velocity of this wave. The application of this result to the radiation of a resonant wave by a soliton-like “core” is discussed. Such radiation occurs in media where classical solitary waves are replaced with generalized solitary waves as a result of linear resonance of long and short waves. Generalized solitary waves are traveling waves that form a homoclinic structure doubly asymptotic to a periodic wave.

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长波和短波共振情况下周期成分辐射的对流调制不稳定性

摘要本文的主要结果是一个定理，说明在任意色散介质中传播的小振幅（但有限）载波周期波的调制不稳定性，只能在以与该波的群速度相差有限的速度运动的参照系中对流。本文讨论了这一结果在类似于孤子 "核心 "的共振波辐射中的应用。由于长波和短波的线性共振，在经典孤波被广义孤波取代的介质中会出现这种辐射。广义孤子波是一种行波，形成与周期波双渐近的同次结构。

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

Proceedings of the Steklov Institute of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.