Hyperbolicity study of the modulation equations for the Benjamin-Bona-Mahony equation

被引：1
|
作者：
Gavrilyuk, Sergey [1 ,3 ]
Lin, Yu-Hsi [1 ]
Shyue, Keh-Ming [2 ]
机构：
[1] Aix Marseille Univ, CNRS, IUSTI, UMR, Marseille, France
[2] Natl Taiwan Univ, Inst Appl Math Sci, Taipei, Taiwan
[3] Aix Marseille Univ, CNRS, UMR 7343, IUSTI, Marseille, France
来源：
STUDIES IN APPLIED MATHEMATICS | 2023年 / 151卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
dispersive equations; modulational instability; MODEL-EQUATIONS; WAVES;
D O I：
10.1111/sapm.12602
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A complete study of the modulation equations for the Benjamin-Bona-Mahony equation is performed. In particular, the boundary between the hyperbolic and elliptic regions of the modulation equations is found. When the wave amplitude is small, this boundary is approximately defined by k=3$k=\sqrt {3}$, where k is the wave number. This particular value corresponds to the inflection point of the linear dispersion relation for the BBM equation. Numerical results are presented showing the appearance of the Benjamin-Feir instability when the periodic solutions are inside the ellipticity region.
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页码：536 / 554
页数：19
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