分数阶Volterra方程
Fractional Volterra Hierarchy
摘要：
证明了满足局部Calabi-Yau条件的三次Hodge积分的生成函数是一个新的可积系统的τ函数，该系统可看作是Volterra格族的分数阶推广，因此我们称之为分数阶Volterra格族.本文利用拉克斯对和Hamilton形式给出了这一可积族的定义，构造了它的τ函数，并给出了它的多孤子解.
英文摘要：
The generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is conjectured to be a tau function of a new integrable system which can be regarded as a fractional generalization of the Volterra lattice hierarchy, so we name it the fractional Volterra hierarchy. In this paper, we give the definition of this integrable hierarchy in terms of Lax pair and Hamiltonian formalisms, construct its tau functions, and present its multi-soliton solutions.
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