© 2015 IOP Publishing Ltd & London Mathematical Society. We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.
- algebraic invariant solution
- Fischer-Kolmogorov equation
- partial differential equation
- polynomial differential equation
- travelling wave