标题： 大振幅稳态旋转孤立波在正常电场下 显示英文标题

标题： Large-Amplitude Steady Rotational Solitary Waves Under Normal Electric Fields

摘要： 本文考虑在正常电场下传播的大振幅、二维和旋转孤立波。 我们提出了一种新的非线性系统模型，该模型由欧拉方程和电势方程控制，具有自由表面。 与之前的工作不同，我们的工作允许内部停滞点和悬垂轮廓。 我们使用解析分岔理论和共形映射证明了大振幅孤立波解的连续曲线的存在性。 此外，为了建立紧性，进行了更复杂的节点分析和Schauder估计，得到了曲线的良好结构。 沿着这条曲线，要么（i）形成极端波并且出现停滞点，要么（ii）自由表面上出现奇异性，或者（iii）无量纲波速变得无界。 显示英文摘要

摘要： This paper considers large-amplitude, two-dimensional and rotational solitary waves propagating under a normal electric field. We present a new model for nonlinear systems with a free surface, governed by Euler and electric potential equations. Unlike previous works, our work allows internal stagnation points and overhanging profiles. We prove the existence of a continuous curve of large-amplitude solitary wave solutions using analytic bifurcation theory and conformal mapping. Furthermore, to establish compactness, more intricate nodal analysis and Schauder estimates are performed, yielding the well-behaved structure of the curve. Along this curve, either (i) an extreme wave forms and the stagnation point occurs, (ii) a singularity emerges on the free surface, or (iii) the dimensionless wave speed becomes unbounded.