if i give a boundary conditions such as

u1(0,t)=u1(1,t)=0;

u2(0,t)=u2(1,t)=0;

u3(0,t)=u3(1,t)=0;

according your steps, what's the value of k1 and k2, and the expression of the u1,u2,u3?

thanx a lot buddy!

thanx for you reply.

but through what's code do you get the solutions of Ansatz:= {u1(x,t)=A*exp(k1*x+k2*t),u2(x,t)=B*exp(k1*x+k2*t), u3(x,t)=C*exp(k1*x+k2*t)}; i trying some command but cannot get the general form of the U(x,t)?
 

thanx for your help. but is your solution

Ansatz:= {u1(x,t)=A*exp(k1*x+k2*t),u2(x,t)=B*exp(k1*x+k2*t), u3(x,t)=C*exp(k1*x+k2*t)};
is numerical solutions then you try to get value of K1 K2 to approximate to an analytical solutions. how can i through the equations to get analytical solutions? thanx for your time.