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Tau Functions of (n,1) curves and Soliton Solutions on Non-Zero Constant Backgrounds (2011.10691v1)
Published 21 Nov 2020 in nlin.SI, math-ph, math.AG, math.MP, and math.QA
Abstract: We study the tau function of the KP-hierarchy associated with an (n,1) curve $yn=x-\alpha$. If $\alpha=0$ the corresponding tau function is 1. On the other hand if $\alpha\neq 0$ the tau function becomes the exponential of a quadratic function of the time variables. By applying vertex opertaors to the latter we obtain soliton solutions on non-zero constant backgrounds.
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