脂肪缝的生长与无分散性KP体系
Growth of fat slits and dispersionless KP hierarchy
摘要：
“胖缝”是上半平面中的紧凑域，其由端点在实轴上的曲线和它们之间的实轴的一段界定。我们认为共形映射的上半平面的外部脂肪缝参数化的谐波矩后者，并表明他们服从一个无限的一组Lax方程的dispersionless KP层次。在特定的简谐矩变化下，厚缝的变形可以看作是一个类似于整个平面上畴的拉普拉斯增长的增长过程。这种结构扩展了公知的解决方案之间的联系dispersionless KP层次和共形映射的狭缝域在上半平面，并提供了一个新的，大家庭的解决方案。
英文摘要：
A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat slit under changing a particular harmonic moment can be treated as a growth process similar to the Laplacian growth of domains in the whole plane. This construction extends the well known link between solutions to the dispersionless KP hierarchy and conformal maps of slit domains in the upper half plane and provides a new, large family of solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
