t := 5;
                               5
u := exp((1/2)*x-2*t*(1/3));
                            /1     10\
                         exp|- x - --|
                            \2     3 /
plot(u(x), x = -4 .. 4);

this is the exact solution graph

while below is the approximate solution graph

h := -1;
                               -1
t := 5;
                               5
u := exp((1/2)*x)*(1+t*(27*h^4+108*h^3+240*h^2+256*h)/2^7+t^2*(27*h^4+24*h^3+168*h^2)/2^7+(1/3)*t^3*(9*h^4+16*h^3)/2^6+(1/4)*t^4*h^4/2^4);
                         6877    /1  \
                         ---- exp|- x|
                         192     \2  /
plot(u(x), x = -4 .. 4);

plot([(exp((1/2)*x))((1/2)*x+2*t*(1/3)), (exp((1/2)*x))(1+t((-256)+240-108+27)/2^7+t(168-24+27)^2/2^7+(1/3)*t^3*((-16)+9)/2^6+(1/4)*t^4/2^7), (exp((1/2)*x))(1+t(256*(-1.01)+240*(-1.01)^2+108*(-1.01)^3+27*(-1.01)^4)/2^7+t(168*(-1.01)^2+24*(-1.01)^3+27*(-1.01)^4)^2/2^7+(1/3)*t^3*(16*(-1.01)^3+9*1.01^4)/2^6+(1/4)*t^4*(-1.01)^4/2^7)], x = -4 .. 4, t = 5)

How can i solve this nonlinear equation using adomian decomposition method in maple? 

utt −uxx +u^2 = 6xt(x^2 −t^2)+x^6t^6