A new application of k-symplectic Lie systems
  The $k$-symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the $k$-symplectic structures to investigate a type of systems of first-order ordinary differential equations, the $k$-symplectic Lie systems. In particular, we analyse the properties, e.g. the superposition rules, of a new example of $k$-symplectic Lie system which occurs in the analysis of diffusion equations. 
J. de Lucas, M. Tobolski and S. Vilari\~no
math-ph math.DG math.MP nlin.SI