论文标题
在第四阶晶格凝胶式 - 二基方程
On the Fourth-Order Lattice Gel'fand-Dikii Equations
论文作者
论文摘要
研究了四阶晶格凝胶式 - 二基方程，以四边形形式进行了研究。利用直接线性化方法，我们提出了扩展晶格凝胶式 - 二基类型的一些方程式。这些方程与四分之一的离散分散关系有关，可以看作是扩展晶格BousSinesQ类型方程的高阶成员。此处给出的结果晶格方程是五组分形式，其中一些是通过引入额外方程式在多维上一致的。通过直接线性化方案以及多维一致的属性讨论了LAX的集成性。考虑了五分量晶格方程的一些减少到四组分形式。
The fourth-order lattice Gel'fand-Dikii equations in quadrilateral form are investigated. Utilizing the direct linearization approach, we present some equations of the extended lattice Gel'fand-Dikii type. These equations are related to a quartic discrete dispersion relation and can be viewed as higher-order members of the extended lattice Boussinesq type equations. The resulting lattice equations given here are in five-component form, and some of them are multi-dimensionally consistent by introducing extra equations. Lax integrability is discussed both by direct linearization scheme and also through multi-dimensional consistent property. Some reductions of the five-component lattice equations to the four-component forms are considered.
