From KP-I Lump Solution to Travelling wave of 3D Gravity Capillary Water wave problem

Speaker: 赖善发 博士, 澳门大学

Inviter: 秦国林

Title: From KP-I Lump Solution to Travelling wave of 3D Gravity Capillary Water wave problem 

Language: Chinese

Time & Venue: 2025.7.9 14:20-15:20  南楼205

Abstract: In this paper, we study the three-dimensional gravity-capillary water-wave problem involving an irrotational, perfect fluid under gravity and surface tension. We focus on steady waves propagating uniformly in one direction. Assuming constant wave speed and water depth, we analyze the fluid's velocity potential and boundary conditions. Using the Kadomtsev-Petviashvili (KP)-I equation as a simplified model, we show that, within a specific parameter range, the problem admits a fully localized solitary-wave solution, consistent with KP-I predictions.