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Bibliographic Details
Main Authors: Daniels, Jake, Nguyen, Nghiem V.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.16756
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_version_ 1866913245245210624
author Daniels, Jake
Nguyen, Nghiem V.
author_facet Daniels, Jake
Nguyen, Nghiem V.
contents In this manuscript, consideration is given to the existence of periodic traveling-wave solutions to the $abcd$-system. This system was derived by Bona, Saut, and Chen to describe small amplitude, long wavelength gravity waves on the surface of water. These exact solutions are formulated in terms of the Jacobi elliptic function cnoidal. The existence of explicit traveling-wave solutions is very useful in theoretical investigations such as stability of solutions, as well as other numerical analysis of the system.
format Preprint
id arxiv_https___arxiv_org_abs_2402_16756
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Exact Jacobi elliptic solutions of the $abcd$-system
Daniels, Jake
Nguyen, Nghiem V.
Analysis of PDEs
35A16, 35A24, 35B10
In this manuscript, consideration is given to the existence of periodic traveling-wave solutions to the $abcd$-system. This system was derived by Bona, Saut, and Chen to describe small amplitude, long wavelength gravity waves on the surface of water. These exact solutions are formulated in terms of the Jacobi elliptic function cnoidal. The existence of explicit traveling-wave solutions is very useful in theoretical investigations such as stability of solutions, as well as other numerical analysis of the system.
title Exact Jacobi elliptic solutions of the $abcd$-system
topic Analysis of PDEs
35A16, 35A24, 35B10
url https://arxiv.org/abs/2402.16756