Page "Differential equation" Paragraph 16

* There are very few methods of solving nonlinear differential equations exactly ; those that are known typically depend on the equation having particular symmetries.

Nonlinear differential equations can exhibit very complicated behavior over extended time intervals, characteristic of chaos.

Even the fundamental questions of existence, uniqueness, and extendability of solutions for nonlinear differential equations, and well-posedness of initial and boundary value problems for nonlinear PDEs are hard problems and their resolution in special cases is considered to be a significant advance in the mathematical theory ( cf.

Navier – Stokes existence and smoothness ).