how to solve kawahara equation?

the numerical solution to a problem involving a nonlinear partial differential equation of the form below

$u_t + uu_x + u_{3x} − u_{5x} = 0$

$u(x, 0) = f (x) , x ∈ R$

which is called Kawahara equation?

I have this adomian solution maple code to solve it but it brings me lots of error

have you any idea?

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Hope that helps. –  vanna Sep 13 '12 at 13:11
What is the meaning of $u_{3x}$ and $u_{5x}$ ? –  doraemonpaul Sep 14 '12 at 2:56
@doraemonpaul : I mean $u_{3x} = {{\partial^3 u\over\partial x^3}}$ 3 times diffrential over u on x –  Mohammad Rafiee Sep 15 '12 at 5:04
@venna : thanks cenrtaily it would –  Mohammad Rafiee Sep 15 '12 at 5:05

You can find the great things in http://www.isrn.com/journals/mp/2012/185469.

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greath thanks to @venna, @doraemonpaul & @sajadi who helped me solve this, the final answer which I expected is as bellow:

In this way I finally could solve it, I did not want to leave this opened in here!

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You can find the solution of Kawahara equation from the research paper http://www.sciencedirect.com/science/article/pii/S0377042709004038#

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