TY - JOUR
T1 - Non-Traveling Wave Solutions of (3+1)-Dimensional Variable Coefficients BLMP Equation with a Compound Technology
AU - Zheng , Xiaoxiao
AU - Xu , Yuanqing
AU - Zhao , Lingling
JO - Journal of Mathematical Study
VL - 3
SP - 253
EP - 274
PY - 2025
DA - 2025/09
SN - 58
DO - http://doi.org/10.4208/jms.v58n3.25.01
UR - https://global-sci.org/intro/article_detail/jms/24407.html
KW - VC-BLMP equation, non-traveling solutions, extended three-wave method, generalized variable separation method.
AB - <p style="text-align: justify;">We investigate non-traveling wave solutions of the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation with time-dependent coefficients, which describes
the propagation of waves in incompressible fluids. We creatively combine the extended three-wave method with the generalized variable separation method and successfully obtain sixty exact non-traveling solutions including kink-like solutions, singular solitary wave-like solutions, periodic solitary wave-like solutions, periodic kink-like solutions, periodic cross-kink-like waves, homoclinic breather wave-like solutions
and so on. The variable coefficients and arbitrary functions in the obtained solutions
are easy to exhibit abundant soliton structures, which may be of great significance
for explaining some practical physical phenomena. By contour plots, 2D plots, and
3D plots, we analyze the dynamic characteristics of periodic cross-kink-like solution,
singular solitary wave-like solution, homoclinic breather wave-like solution. Additionally, we show changes of solutions under different tails to illustrate the influence
of tails on solutions.</p>