Evolution of Nonlinear Periodic Waves in the Focusing and Defocusing Cylindrical Modified Korteweg-de Vries Equations

Nese Ozdemir; Ali Demirci; Semra Ahmetolan

doi:10.1007/s10773-024-05841-2

Evolution of Nonlinear Periodic Waves in the Focusing and Defocusing Cylindrical Modified Korteweg-de Vries Equations

Nese Ozdemir^*, Ali Demirci, Semra Ahmetolan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

This study investigates the evolution of dispersive shock wave (DSW) solutions within the focusing and defocusing cylindrical modified Korteweg-de Vries (cmKdV(f)) and (cmKdV(d)) equations under Riemann-type initial conditions. Using Whitham modulation theory, we derive and numerically solve the Whitham systems, enabling a comparison between these asymptotic solutions and direct numerical simulations of the cmKdV equations. The results provide a detailed classification of wave structures in both focusing and defocusing cases of the cmKdV equations. This research offers new insights into the behavior and classification of nonlinear periodic waves in the cmKdV equations.

Original language	English
Article number	300
Journal	International Journal of Theoretical Physics
Volume	63
Issue number	12
DOIs	https://doi.org/10.1007/s10773-024-05841-2
Publication status	Published - Dec 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

Keywords

Dispersive shock waves
Focusing and defocusing cylindrical modified KdV equations
Riemann problem classification
Whitham modulation theory

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10.1007/s10773-024-05841-2

Cite this

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title = "Evolution of Nonlinear Periodic Waves in the Focusing and Defocusing Cylindrical Modified Korteweg-de Vries Equations",

abstract = "This study investigates the evolution of dispersive shock wave (DSW) solutions within the focusing and defocusing cylindrical modified Korteweg-de Vries (cmKdV(f)) and (cmKdV(d)) equations under Riemann-type initial conditions. Using Whitham modulation theory, we derive and numerically solve the Whitham systems, enabling a comparison between these asymptotic solutions and direct numerical simulations of the cmKdV equations. The results provide a detailed classification of wave structures in both focusing and defocusing cases of the cmKdV equations. This research offers new insights into the behavior and classification of nonlinear periodic waves in the cmKdV equations.",

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AU - Ozdemir, Nese

AU - Demirci, Ali

AU - Ahmetolan, Semra

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2024/12

Y1 - 2024/12

N2 - This study investigates the evolution of dispersive shock wave (DSW) solutions within the focusing and defocusing cylindrical modified Korteweg-de Vries (cmKdV(f)) and (cmKdV(d)) equations under Riemann-type initial conditions. Using Whitham modulation theory, we derive and numerically solve the Whitham systems, enabling a comparison between these asymptotic solutions and direct numerical simulations of the cmKdV equations. The results provide a detailed classification of wave structures in both focusing and defocusing cases of the cmKdV equations. This research offers new insights into the behavior and classification of nonlinear periodic waves in the cmKdV equations.

AB - This study investigates the evolution of dispersive shock wave (DSW) solutions within the focusing and defocusing cylindrical modified Korteweg-de Vries (cmKdV(f)) and (cmKdV(d)) equations under Riemann-type initial conditions. Using Whitham modulation theory, we derive and numerically solve the Whitham systems, enabling a comparison between these asymptotic solutions and direct numerical simulations of the cmKdV equations. The results provide a detailed classification of wave structures in both focusing and defocusing cases of the cmKdV equations. This research offers new insights into the behavior and classification of nonlinear periodic waves in the cmKdV equations.

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Evolution of Nonlinear Periodic Waves in the Focusing and Defocusing Cylindrical Modified Korteweg-de Vries Equations

Abstract

Bibliographical note

Keywords

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