A Classification of Integrable Quasiclassical Deformations of Algebraic   Curves
  A previously introduced scheme for describing integrable deformations of of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic type systems. A general solution of the compatibility conditions for consistent deformations is given and expressions for the solutions of the corresponding Lenard relations are provided. 
B. Konopelchenko, L. Martinez Alonso and E. Medina