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

共 31 条

[1] Waves that appear from nowhere and disappear without a trace [J].

Akhmediev, N. ;

Ankiewicz, A. ;

Taki, M. .

PHYSICS LETTERS A, 2009, 373 (06) :675-678

[2] Extended criterion for the modulation instability [J].

Amiranashvili, Shalva ;

Tobisch, Elena .

NEW JOURNAL OF PHYSICS, 2019, 21 (03)

[3] Baseband modulation instability as the origin of rogue waves [J].

Baronio, Fabio ;

Chen, Shihua ;

Grelu, Philippe ;

Wabnitz, Stefan ;

Conforti, Matteo .

PHYSICAL REVIEW A, 2015, 91 (03)

[4] On the generation of solitons and breathers in the modified Korteweg-de Vries equation [J].

Clarke, S ;

Grimshaw, R ;

Miller, P ;

Pelinovsky, E ;

Talipova, T .

CHAOS, 2000, 10 (02) :383-392

[5]

[Диденкулова Екатерина Геннадьевна Didenkulova Ekaterina Gennadievna], 2019, [Вычислительные технологии, Vychislitel'nye tekhnologii], V24, P52

[6]

Drazin P.G., 1993, Solitons, An Introduction

[7] Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity [J].

Friedman, Isaac ;

Riano, Oscar ;

Roudenko, Svetlana ;

Son, Diana ;

Yang, Kai .

NONLINEARITY, 2023, 36 (01) :584-635

[8] KORTEWEG-DEVRIES EQUATION AND GENERALIZATIONS .6. METHODS FOR EXACT SOLUTION [J].

GARDNER, CS ;

GREENE, JM ;

KRUSKAL, MD ;

MIURA, RM .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1974, 27 (01) :97-133

[9] Robustness of the absolute Rosenau-Hyman |K |(p, p) equation with non-integer p [J].

Garralon-Lopez, Ruben ;

Rus, Francisco ;

Villatoro, Francisco R. .

CHAOS SOLITONS & FRACTALS, 2023, 169

[10] Wave group dynamics in weakly nonlinear long-wave models [J].

Grimshaw, R ;

Pelinovsky, D ;

Pelinovsky, E ;

Talipova, T .

PHYSICA D-NONLINEAR PHENOMENA, 2001, 159 (1-2) :35-57

← 1 2 3 4 →