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

الملخص EN

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.