The FritzHugh-Nagomo equation occurs in many apps such as biology, genetics and heat transfer. In the 1-D case, it can be written as
du/dt = d^2/dx^2 + u(u-1)(λ-u)
where λ is constant. Show that this eqn supports a travelling wave
u(x,t) =(Ae^n1 + λBe^n2)/(Ae^n1 + Be^n2 + k)
where
n1 = (1/λ - λ)t +- x/√2
n2 = λ(λ/2 - 1)t +- λx/√2
and A,B and k are orbitrary constant.