论文标题
关于非本地$ \叠加{\ partial} $问题的解决方案和（2+1）尺寸完全可集成的系统
On Solutions to the Nonlocal $\overline{\partial}$ Problem and (2+1) Dimensional Completely Integrable Systems
论文作者
论文摘要
在此简短的说明中，我们讨论了一个新的公式，用于解决非本地$ \ edline {\ partial} $ - 问题，并讨论对Manakov-Zakharov Dressing方法的应用。然后，我们将此公式明确地应用于求解复合物（2+1）d kadomtsev--petviashvili方程和复合物（2+1）d（2+1）d kaup--broer（或kaup--boussinesq）系统的完全可以整合的概括。我们还将讨论如何使用这种形式主义表达真实的（1+1）d解决方案。使用本注释的形式主义来表达[10] [8]的有限差距原始解决方案的形式主义。我们还讨论了（1+1）d Korteweg-de Vries方程和（2+1）d kaup-broer系统的无限孤子极限的最新结果。在附录中，描述了惠特克（Whittaker）介绍了3D拉普拉斯方程（2+1）d d'Alembt Wave方程的经典解决方案。包括此附录是为了阐明调皮方法与惠特克解决方案之间的类比。
In this short note we discuss a new formula for solving the nonlocal $\overline{\partial}$-problem, and discuss application to the Manakov--Zakharov dressing method. We then explicitly apply this formula to solving the complex (2+1)D Kadomtsev--Petviashvili equation and complex (2+1)D completely integrable generalization of the (2+1)D Kaup--Broer (or Kaup--Boussinesq) system. We will also discuss how real (1+1)D solutions are expressed using this formalism. It is simple to express the formalism for finite gap primitive solutions from [10], [8] using the formalism of this note. We also discuss recent results on the infinite soliton limit for the (1+1)D Korteweg--de Vries equation and the (2+1)D Kaup--Broer system. In an appendix, the classical solutions to the 3D Laplace equation (2+1)D d'Alembert wave equation by Whittaker are described. This appendix is included to elucidate an analogy between the dressing method and the Whittaker solutions.
