A new $(\gamma_n,\sigma_k)-$ KP hierarchy and generalized dressing method
Yuqin Yao, Yehui Huang, Yunbo Zeng
TL;DR
This paper introduces a novel (rac{\gamma_n}{\sigma_k})-KP hierarchy with new time series, explores its reductions and constrained flows, and generalizes the dressing method to generate solutions.
Contribution
It proposes a new (rac{\gamma_n}{\sigma_k})-KP hierarchy, studies its reductions, and extends the dressing method for solution construction.
Findings
Defined the (rac{\gamma_n}{\sigma_k})-KP hierarchy with new flows.
Analyzed reductions and constrained flows of the hierarchy.
Generalized the dressing method to this new hierarchy.
Abstract
A new (\gamma_n,\sigma_k)-KP hierarchy with two new time series \gamma_n and \sigma_k, which consists of \gamma_n-flow, \sigma_k-flow and mixed \gamma_n and \sigma_k evolution equations of eigenfunctions, is proposed. Two reductions and constrained flows of (\gamma_n,\sigma_k)-KP hierarchy are studied. The dressing method is generalized to the (\gamma_n,\sigma_k)-KP hierarchy and some solutions are presented.
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