论文标题
在2D可集成的晶格方程中
On a class of 2D integrable lattice equations
论文作者
论文摘要
我们开发了一种新方法，以分类$ u_ u_ {xy} = f（u，u _x，u_y，u_y，\ triangle_z u \ triangle _ {\ bar z} u，\ bar z} u，\ triangle_ {z \ bar z}向前/后退离散衍生物。提出了以下两步分类程序： （1）首先，我们要求方程式的无分散极限是可以集成的，即其特征性变体定义了共形结构，在每个溶液上都是Einstein-Weyl。 （2）其次，在上一步中选择的候选方程式，我们应用了通过施加合适的截止条件获得的Darboux集成性的测试。
We develop a new approach to the classification of integrable equations of the form $$ u_{xy}=f(u, u_x, u_y, \triangle_z u \triangle_{\bar z}u, \triangle_{z\bar z}u), $$ where $\triangle_{ z}$ and $\triangle_{\bar z}$ are the forward/backward discrete derivatives. The following 2-step classification procedure is proposed: (1) First we require that the dispersionless limit of the equation is integrable, that is, its characteristic variety defines a conformal structure which is Einstein-Weyl on every solution. (2) Secondly, to the candidate equations selected at the previous step we apply the test of Darboux integrability of reductions obtained by imposing suitable cut-off conditions.
