Links between (γn,σk)-KP Hierarchy, (γn,σk)-mKP Hierarchy, and (2+1)-(γn,σk)-Harry Dym Hierarchy

Abstract

The new (2+1)-(γn,σk)-Harry Dym hierarchy and (γn,σk)-mKP hierarchy with two new time series γn and σk, which consist of γn-flow, σk-flow, and mixed γn and σk evolution equations of eigenfunctions, are proposed. Gauge transformations and reciprocal transformations between (γn,σk)-KP hierarchy, (γn,σk)-mKP hierarchy, and (2+1)-(γn,σk)-Harry Dym hierarchy are studied. Their soliton solutions are presented.