发表机构
Central China Normal University; Nankai University（华中师范大学; 南开大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文首次构造了全二维有限水深水波问题中的非对称周期解族，涵盖纯重力与毛细-重力情形，填补了该领域空白。
AI 中文摘要
本文首次构造了全二维有限水深水波问题中非对称周期解族，涵盖纯重力与毛细-重力情形。
英文摘要
We consider the full two-dimensional water-wave equations in finite depth, with and without surface tension. Water waves have been studied mathematically for more than two centuries. Reflection symmetry remains a common assumption in constructions of periodic steady waves, although asymmetric profiles have been observed in experiments and numerical computations. We construct families of periodic stationary solutions whose free surfaces have no axis of reflection, in both the pure-gravity and capillary--gravity cases. To the best of our knowledge, this provides the first rigorous construction of asymmetric periodic pure-gravity waves for the full two-dimensional water-wave problem in finite depth. The proof combines localized vorticity laws with a Lyapunov--Schmidt reduction. In the pure-gravity case, we introduce a small background shear flow to obtain an invertible boundary operator and couple the interior and free-surface approximations at leading order.
