I have a system of pdes and i'm trying to find some travelling waves solution. the system is: ( s=s(x,t), i=i(x,t)

D[s[x,t],t]=s(1-s-i)
D[i[x,t],t]=alfa*i*(s-lambda)+D[i[x,t],x,x]

steady states of interest (lambda, 1-lambda), (1,0)

by putting z=x+ct and differentiating respect to z I find:

   c*s'[z]=s(1-s[z]-i[z])
   i'[z]=w[z]
   w'[z]=c*w[z]-alfa*i[z]*(s[z]-lambda)

now i want to solve this system of odes in whic the boundary condition are given by: s(-inf)=1 s(+inf)=lambda i(-inf)=0 i(+inf)=1-lambda and all the derivatives al +inf and -inf are equal to 0 to satify the steady state conditions;

any thoughts on how i could plot s and i over z?

Thank you