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Pure Mathematics 2024
椭圆链式KP系统的可积性分析
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Abstract:
我们以前已经深入研究了求解椭圆链式KP方程的直接线性化方法，而求解该方程的柯西矩阵方法只是近年来的一个热门主题。本文将讨论基于柯西矩阵方法的椭圆链式KP方程的可积性，为下一步的求解做准备。本文首先从辅助向量u(2i)=(IXC)？1Pic出发得到椭圆链式KP系统的lax组，然后从Lax组中推导出椭圆链式KP系统来完成闭环。
We have previously delved into direct linearization methods for solving the elliptic lattice KP system, and the Cauchy matrix method for solving this equation has only been a hot topic in recent years. This article will discuss the integrability of the elliptic lattice KP system based on the Cauchy matrix method, in preparation for the next step of solution. Firstly, starting from the auxiliary vectoru(2i)=(IXC)？1Pic, we obtain the lax system of the elliptic lattice KP system, and then derive the elliptic lattice KP system from the lax system to complete the closed-loop process.
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