Nonlinear waves, modulations and rogue waves in the modular Korteweg-de Vries equation

被引：6

作者：

Slunyaev, A. V. ^{[1
,2
]}

Kokorina, A. V. ^{[2
]}

Pelinovsky, E. N. ^{[1
,2
]}

机构：

[1] Natl Res Univ Higher Sch Econ, Nizhnii Novgorod, Russia

[2] Russian Acad Sci, Inst Appl Phys, Nizhnii Novgorod, Russia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2023年 / 127卷

基金：

俄罗斯科学基金会;

关键词：

Modular Korteweg-de Vries equation; Quadratically cubic Korteweg-de Vries equation; Modular envelope equation; Quadratically cubic nonlinear schrodinger equation; Envelope solitons; Modulational instability; Modular rogue waves; GENERATION; SOLITONS; DYNAMICS;

D O I：

10.1016/j.cnsns.2023.107527

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Effects of nonlinear dynamics of solitary waves and wave modulations within the modular (also known as quadratically cubic) Korteweg-de Vries equation are studied analytically and numerically. Large wave events can occur in the course of interaction between solitons of different signs. Stable and unstable (finite-time-lived) breathers can be generated in inelastic collisions of solitons and from perturbations of two polarities. A nonlinear evolution equation on long modulations of quasi-sinusoidal waves is derived, which is the modular or quadratically cubic nonlinear Schrodinger equation. Its solutions in the form of envelope solitons describe breathers of the modular Korteweg-de Vries equation. The instability conditions are obtained from the linear stability analysis of periodic wave perturbations. Rogue-wave-type solutions emerging due to the modulational instability in the modular Korteweg-de Vries equation are simulated numerically. They exhibit similar wave amplification, but develop faster than in the Benjamin-Feir instability described by the cubic nonlinear Schrodinger equation. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：18