Evolution of initial discontinuity for the defocusing complex modified KdV equation

The complete classification of solutions to the defocusing complex modified Korteweg-de Vries (cmKdV) equation with the step-like initial condition is given by Whitham theory. The process of studying the solution of cmKdV equation can be reduced to explore four quasi-linear equations, which predicts...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2019-10, Vol.98 (1), p.691-702
Main Authors: Kong, Liang-Qian, Wang, Lei, Wang, Deng-Shan, Dai, Chao-Qing, Wen, Xiao-Yong, Xu, Ling
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Classification
Computer simulation
Control
Defocusing
Dynamical Systems
Engineering
Evolution
Fluid mechanics
Korteweg-Devries equation
Linear equations
Mechanical Engineering
Original Paper
Rarefaction
Schrodinger equation
Shock waves
Vibration
Wave dispersion
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The complete classification of solutions to the defocusing complex modified Korteweg-de Vries (cmKdV) equation with the step-like initial condition is given by Whitham theory. The process of studying the solution of cmKdV equation can be reduced to explore four quasi-linear equations, which predicts the evolution of dispersive shock wave. The results obtained here are quite different from the defocusing nonlinear Schrödinger equation: the bidirectionality of defocusing nonlinear Schrödinger equation determines that there are two basic rarefaction and shock structures while in the cmKdV case three basic rarefaction structures and four basic dispersive shock structures are constructed which lead to more complicated classification of step-like initial condition, and wave patterns even consisted of six different regions while each of wave patterns is consisted of five regions in the defocusing nonlinear Schrödinger equation. Direct numerical simulations of cmKdV equation are agreed well with the solutions corresponding to Whitham theory.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-05222-z