Conservation laws and associated Noether type vector fields via partial Lagrangians and Noether's theorem for the Liang equation

We show how one can construct conservation laws of the Liang equation which is not variational but may be regarded as Euler-Lagrange in part. This first requires the determination of the Noether-type symmetries associated with the partial Lagrangian. The final construction of the conservation laws resort to a formula equivalent to Noether's theorem. A variety of subclasses are given and, for each, a large number of conserved flows are found-the method is usable for any general choice of the variable speed of sound.