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Pure Mathematics 2024
KP方程新解与τ函数的联系
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Abstract:
τ函数在非线性方程的双线性化中发挥重要作用。本文从Sylvester方程出发，结合色散关系用柯西矩阵法先推出KP方程，并求出KP方程的解，其中KP方程的解是矩阵乘积形式。接着建立KP方程的解与τ函数之间的联系，从而建立柯西矩阵法求解与双线性法求解之间的联系。
τ functions play an important role in bilinearization of nonlinear equations. Starting from the Sylvester equation and combining dispersion relationships, this article first derives the KP equation using the Cauchy matrix method, and obtains the solution of the KP equation. The solution of the KP equation is in matrix product form. Then, the relationship between the solution of the KP equation and the function is established, thereby establishing the relationship between Cauchy matrix method and bilinear method solution.
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