%0 Journal Article
%T 具有时空卷积的Wazwaz-Benjamin-Bona-Mahony方程孤立波和周期波的不存在性<br>Non-Existence of Solitary Wave and Periodic Wave for Wazwaz-Benjamin-Bona-Mahony Equation with Spatiotemporal Convolution
%A 周笑笑
%J Advances in Applied Mathematics
%P 29-39
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.145230
%X 本文研究具有时空卷积的Wazwaz-Benjamin-Bona-Mahony (WBBM)方程孤立波和周期波的存在性。根据几何奇异摄动理论&#65292;将一个非线性偏微分方程转化为平面二维动力系统。基于Melnikov方法&#65292;可以判断出扰动WBBM方程的孤立波和周期波是不存在的。<br>This paper discusses the existence of solitary waves and periodic waves for Wazwaz-Benjamin-Bona-Mahony (WBBM) equation with spatiotemporal convolution. According to the theory of geometric singular perturbations, a nonlinear partial differential equation is transformed into a two-dimensional planar dynamical system. Based on the Melnikov method, it can be determined that solitary waves and periodic waves of perturbed WBBM equation do not exist.
%K Wazwaz-Benjamin-Bona-Mahony方程&#65292
%K 几何奇异摄动&#65292
%K 孤立波解&#65292
%K 周期波解&#65292
%K Melnikov积分<br>Wazwaz-Benjamin-Bona-Mahony Equation
%K Geometric Singular Perturbation
%K Solitary Wave Solution
%K Periodic Wave Solution
%K Melnikov Integral
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=113848