Boundary Condition at infinity for a non linear odes system

I have a system of pdes and i'm trying to find some travelling waves solution. the system is:

    s |t|=s(1-s-i)
    i |t|=alfa*i*(s-lambda)+i |xx|

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

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

   c*s'=s(1-s-i)
   i'=w
   w'=c*w+alfa*i*(s-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