Critical wave speeds for a family of scalar reaction-diffusion equations (Q5938881)

The authors study travelling wave solutions of the scalar bistable reaction-diffusion equation NEWLINE\[NEWLINE{\partial u\over\partial t}= {\partial^2u\over\partial x^2}+ F(u, \omega),NEWLINE\]NEWLINE where \(F(u,\omega)= f(u)- \omega\), and \(\omega\) is a control parameter, \(f(u)= 2u^m(1- u)\), \(m> 1\). They present analytic results for the properties of the critical value of wave speed, that separates solutions with algebraic and exponential structure of \(f(u)\). Note that potential \(f(u)\) includes the classic cubic potentials, that is \(m=2\), and Fischer's equations \(m=1\).