论文标题
离散的BousSinesQ型方程
Discrete Boussinesq-type equations
论文作者
论文摘要
我们根据基础四边形上的三组分形式对离散的BousSinesQ方程进行了全面的综述。这些方程最初是由Nijhoff等人使用直接线性化方法发现的，后来又通过基于多维一致性的搜索方法概括了Hietarinta。我们从这些三组分方程中得出它们的两个组成型变体。从单一组件形式来看，我们得出了两个不同的半连续限制及其完全连续的限制，这些极限原来是常规，修改和schwarzian boussinesq方程的PDE。还提供了几种宽松对。最后，我们从Casoratians提出了他们的野田双线性形式和多苏利顿解决方案。
We present a comprehensive review of the discrete Boussinesq equations based on their three-component forms on an elementary quadrilateral. These equations were originally found by Nijhoff et al using the direct linearization method and later generalized by Hietarinta using a search method based on multidimensional consistency. We derive from these three-component equations their two- and one-component variants. From the one-component form we derive two different semi-continuous limits as well as their fully continuous limits, which turn out to be PDE's for the regular, modified and Schwarzian Boussinesq equations. Several kinds of Lax pairs are also provided. Finally we give their Hirota bilinear forms and multi-soliton solutions in terms of Casoratians.
