TY - JOUR
T1 - Traveling Wave Solutions of Some $abcd$-Water Wave Models Describing Small Amplitude, Long Wavelength Gravity Waves on the Surface of Water
AU - Li , Jibin
AU - Shi , Zhilong
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 1125
EP - 1141
PY - 2025
DA - 2025/05
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1125
UR - https://global-sci.org/intro/article_detail/jnma/24119.html
KW - Pseudo-peakon, solitary wave, kink and anti-kink wave, compacton family, planar dynamical system, $abcd$-water wave models.
AB - <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>