Tropical Differential Equations

Tropical differential equations are introduced. Similar to usual
tropical algebraic equations which provide necessary conditions for
solvability of systems of polynomial equations in Puiseux series,
tropical differential equations express necessary conditions for
solvability of systems of differential equations in power (or Hahn)
series.

For a system of tropical linear differential equations we prove the
existence of the minimal among its solutions. A polynomial
complexity algorithm is designed for solving such systems. For
tropical non-linear differential systems its NP-completeness is
established.

Several open questions are supposed to be discussed.