Step-like initial value problem and Whitham modulation in fluid dynamics to a generalized derivative nonlinear Schrödinger equation

In this paper, we study the step-like initial value problem for a generalized derivative nonlinear Schrödinger equation using the Whitham modulation theory. First, we utilize the finite-gap integration method to obtain the periodic solutions and the relevant Whitham equations for the 0-, 1-, and 2-g...

Full description

Saved in:
Bibliographic Details
Published inPhysics of fluids (1994) Vol. 36; no. 6
Main Authors Liu, Bingyu, Zhao Qiulan, Li Xinyue
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.06.2024
Subjects
Boundary value problems
Fluid dynamics
Modulation
Parameters
Rarefaction
Schrodinger equation
Shock waves
Online AccessGet full text

Cover

More Information
Summary:In this paper, we study the step-like initial value problem for a generalized derivative nonlinear Schrödinger equation using the Whitham modulation theory. First, we utilize the finite-gap integration method to obtain the periodic solutions and the relevant Whitham equations for the 0-, 1-, and 2-genus cases used to characterize dispersive shock waves (DSWs). Second, we investigate four fundamental waves: two rarefaction waves (RWs) and two DSWs with step-like initial data. On this basis, we show the effect of varying certain parameters on the dynamics of the fluid model. We find that the boundary value, amplitude, and shape of the wave pattern in the fluid dynamics model will be significantly impacted by these parameters. Third, under two step-like initial data, waves are divided into six cases, which are actually combinations of DSWs and RWs. Finally, the dam break problem is explored to prove the effectiveness of the Whitham modulation theory in physical applications.
ISSN:1070-6631
1089-7666
DOI:10.1063/5.0210864