离散Schwarzian KdV方程的双线性化和特解
Bilinearization and Special Solutions to the Discrete Schwarzian KdV Equation
摘要：
讨论了离散Schwarzian KdV方程的各种解。首先导出离散Schwarzian KP方程的Hirota型双线性差分方程，并将其分解为三个离散的二维Toda格点方程。然后，我们构造两种解决方案的Casorati行列式。我们导出了非均匀格点上的离散Schwarzian KdV方程及其约化过程的解。最后讨论了Painlevé系统的$τ$函数解.
英文摘要：
Various solutions to the discrete Schwarzian KdV equation are discussed. We first derive the bilinear difference equations of Hirota type of the discrete Schwarzian KP equation, which is decomposed into three discrete two-dimensional Toda lattice equations. We then construct two kinds of solutions in terms of the Casorati determinant. We derive the discrete Schwarzian KdV equation on an inhomogeneous lattice and its solutions by a reduction process. We finally discuss the solutions in terms of the $τ$ functions of some Painlevé systems.
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