# Nonlinear pdes system / boundary condition at infinity

Posted 8 years ago
9409 Views
|
3 Replies
|
0 Total Likes
|
 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
3 Replies
Sort By:
Posted 8 years ago
 I don't think this one is easy to solve, the infinite domain makes it harder.
Posted 8 years ago
 There seem to be inconsistencies in your equations: shouldn't it be w'=c w - alpha i (s- lambda) ?
Posted 8 years ago
 yes i missed that typo thank you, but still i cannot get any reasonable solution!