ON TRAVELING WAVES OF A GENERALIZED BISTABLE EQUATION

1. IntroductionConsider the initial value problem for the bistable equationwhere f(u) = u(1-u)(u-a) and 0 < 2a < 1. Let us examine the critical points of f. Sincethe critical points are given by ρ±(a)=1/3(1 a± √1-a a~2),which are functions of theparameter a and satisfy ρ(a) ρ-(a) =2 2a/3 andρ p (a)ρ-(a)= a/3. Sinceone can obtain the ranges of the critical points 0 < ρ-(a) <1/4, 2/3 <ρ (a) <4/5. For anyconstant w with f(ρ-(a)) < w < f(ρ (a)), suppose that f(u) - w = -(u - A)(u …