sol61115 = NDSolve[{D[u1[x, t], t] == 1*D[u1[x, t], {x, 2}] - 1*u1[x, t]^2/(u1[x, t]^2 + 1^2) - 1*u1[x, t]^2/(u1[x, t]^2 + 1^2) + 1*1*Exp[((1*1^2/(1^2 + 1^2) + 1 - 1))/1] + 1*1*1*u1[x, t]^2*u2[x, t]^2* u3[x, t]/((u1[x, t]^2 + 1^2)*(u2[x, t]^2 + 1^2)) + 1*1*1*u1[x, t]^2*u2[x, t]^2* u4[x, t]/((u1[x, t]^2 + 1^2)*(u2[x, t]^2 + 1^2)),(*1式*) D[u2[x, t], t] == 1*D[u2[x, t], {x, 2}] - (1*1/(1 + 1))*u1[x, t]/(u1[x, t] + 1) - 1*u2[x, t],(*2式*)(*边界条件*) 1*D[u3[x, t], t] == 1^2/(1^2 + u1[x, t]^2) - u3[x, t], 1*D[u4[x, t], t] == 1^2/(1^2 + u1[x, t]^2) - u4[x, t], D[u1[0, t], t] == 0, D[u1[1, t], t] == 0, D[u2[0, t], t] == 0, D[u1[1, t], t] == 0},(*初值条件*){u1, u2, u3, u4}, {x, 0, 1}, {t, 0, 1}]