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首页> 外文期刊>Progress of Theoretical Physics >Solutions for the Mikhailov-Shabat-Yamilov difference-differential equations and generalized solutions for the Volterra and the Toda lattice equations
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Solutions for the Mikhailov-Shabat-Yamilov difference-differential equations and generalized solutions for the Volterra and the Toda lattice equations

机译：Mikhailov-Shabat-Yamilov差分方程的解以及Volterra和Toda晶格方程的广义解

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摘要

We present two types of mixed 1-rational N-soliton solutions and two types of special solutions for four types of Volterra-related difference-differential equations arising in Mikhailov, Shabat and Yamilov's lists. We also find new expressions of mixed 1-rational N-soliton solutions for the Volterra and the Toda lattice equations based on the invariance of Gibbon and Tabor's equation (J. Math. Phys. 26 (1985), 1956) under the fractional linear transfermation. By taking appropriate limits of wave numbers, we find some new rational solutions for the Volterra and the Toda lattice equations. We also present elliptic function solutions for the Volterra and the Toda lattice equations different from known ones based on the same formulation. [References: 27]
机译：对于在Mikhailov，Shabat和Yamilov的列表中出现的四种与Volterra相关的差分-微分方程，我们给出了两种类型的混合的1-理性N-孤子解和两种类型的特殊解。我们还基于分数线性转移条件下基于Gibbon和Tabor方程的不变性（J. Math。Phys。26（1985），1956）为Volterra和Toda晶格方程找到了混合的1比率N孤子解的新表达式。 。通过适当地限制波数，我们为Volterra和Toda晶格方程找到了一些新的有理解。我们还提供了基于相同公式的不同于已知方程的Volterra和Toda晶格方程的椭圆函数解。 [参考：27]

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