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首页> 外文期刊>Communications in Mathematical Physics >A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations
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A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations

机译:可积四边形格子方程孤子解的一种构造方法

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Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the B?cklund transformation, and the method of solving a Riccati map by exploiting two known particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler's lattice equation (or Q4).
机译:研究了标量多维一致的四边形格子方程。我们探索了由B?cklund变换相关的解的叠加原理与通过利用两个已知的特定解来求解Riccati映射的方法之间的融合。这导致该类内泛型方程的N个孤子类型解的表达式。作为一个特殊的例子,我们为主要模型给出了一个明确的N孤子解,这是Adler的晶格方程(或Q4)。

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