@Article{JNMA-7-1125,
author = {Li , Jibin and Shi , Zhilong},
title = {Traveling Wave Solutions of Some $abcd$-Water Wave Models Describing Small Amplitude, Long Wavelength Gravity Waves on the Surface of Water},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2025},
volume = {7},
number = {3},
pages = {1125--1141},
abstract = {<p style="text-align: justify;">For some $abcd$-water wave models describing small amplitude, long
wavelength gravity waves on the surface of water, in this paper, by using the
method of dynamical systems to analyze corresponding traveling wave systems
and find the bifurcations of phase portraits, the dynamical behavior of systems
can be derived. Under some given parameter conditions, for a wave component,
the existence of periodic wave solutions, solitary wave solutions, kink and anti-kink wave solutions as well as compacton families can be proved. Possible exact
explicit parametric representations of the traveling wave solutions are given.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2025.1125},
url = {http://global-sci.org/intro/article_detail/jnma/24119.html}
}