Mathematical Sciences: Study of Nonlinear Problems by the IST Method

该项目支持一组 克拉克森大学的美国科学家和一群俄罗斯科学家 来自列宁格勒大学的科学家。 该研究涉及 用逆方法研究非线性偏微分方程 散射变换（IST）方法。 IST方法是一种 1+1（一个空间）中成功而有力的求解方法 和一个时间维度）设置。 IST方法的力量来自于 从某个非线性偏微分方程的解 微分方程可以归结为解 线性常微分方程的反问题，以及 这样的逆问题通常可以用公式表示为Riemann- 希尔伯特问题 因此，某些非线性方程的解 偏微分方程已得到简单地通过使用 解线性微分方程的方法。 的 将IST方法推广到N+1，其中N大于1， 并不成功，到目前为止，一些结果只 求出N=2。 列宁格勒的俄罗斯队被认为是 在这个科学领域的世界顶尖团队。 一 合作将对美国有重大的科学优势。 科学家 这项美苏合作所支持的科学是在 偏微分方程的一般区域 本研究 主题涉及运动方程、流体流动、物理等。 来模拟我们的物理宇宙。

This project supports the collaboration between a group of U.S. scientists at Clarkson University and a group of Russian scientists from University of Leningrad. The research concerns the study of nonlinear partial differential equations by the Inverse Scattering Transform (IST) Method. The IST method has been a successful and powerful method of solution in the 1+1 (one space and one time dimension) setting. The power of the IST method comes from the fact that the solution of certain nonlinear partial differential equations can be reduced to the solution of the inverse problem for linear ordinary differential equations, and such an inverse problem can usually be formulated as a Riemann- Hilbert problem. As a result, the solution of certain nonlinear partial differential equations have been obtained simply by using the methods to solve linear differential equations. The generalization of the IST method to N+1, where N is greater than 1, has not been as successful and so far some results have only been obtained for N=2. The Russian team at Leningrad is noted as one of the top teams in the world in this area of science. A collaboration would have significant scientific advantage to U.S. scientists. The science supported in this US-USSR collaboration is in the general area of partial differential equations. This research topic concerns the equations of motion, fluid flow, physics, etc. that model our physical universe.