Nonhomogeneous hydrodynamic-type equations and their superextension

Abstract

It is observed that some (x,t) interchanged nonlinear integrable system do have the characteristics of nonhomoneous integrable system of hydrodynamic type. The second Hamiltonian structure obtained through the Miura map or Lie derivative with respect to the master symmetry do have the requisite features. In the present communication we study the cases of dispersive water wave and NLS equation with (x,t) interchanged. Along with these we also analyse the case of supersymmetric version of the (x,t) interchanged KdV problem which yields an example of a super hydrodynamics system.