标题： KP孤子、完全正性和簇代数 显示英文标题

标题： KP solitons, total positivity, and cluster algebras

摘要： Kadomtsev和Petviashvili在1970年提出了现在被称为KP方程的二维非线性色散波方程，自那时以来，KP方程的孤子解一直被研究。众所周知，KP方程的Wronskian方法提供了一种构造孤子解的方法。通过这种方式获得的规则孤子解来自于格拉斯曼流形的完全非负部分。在本文中，我们解释了总正性和簇代数理论如何为理解KP方程的这些孤子解提供了一个框架。然后，我们利用这个框架来给出某些孤子轮廓图的显式构造，并解决了来自格拉斯曼流形的完全正部分的孤子解的逆问题。 显示英文摘要

摘要： Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solutions that one obtains in this way come from points of the totally non-negative part of the Grassmannian. In this paper we explain how the theory of total positivity and cluster algebras provides a framework for understanding these soliton solutions to the KP equation. We then use this framework to give an explicit construction of certain soliton contour graphs, and solve the inverse problem for soliton solutions coming from the totally positive part of the Grassmannian.