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 seriesγnandσk, which consist ofγn-flow,σk-flow, and mixedγnandσkevolution 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.