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
Non-Existence of Solitary Wave and Periodic Wave for Wazwaz-Benjamin-Bona-Mahony Equation with Spatiotemporal Convolution
摘要: 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，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，可以判断出扰动WBBM方程的孤立波和周期波是不存在的。
Abstract: 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.
文章引用：周笑笑. 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[J]. 应用数学进展, 2025, 14(5): 29-39. https://doi.org/10.12677/aam.2025.145230

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