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Question: problem using DEtools [rifsimp]

Question:problem using DEtools [rifsimp]

alaloush 35 Maple 2018
pde detools differential-equations rifsimp
September 19 2019
1

 

Hello all
I'm working on calculating the conservation laws for a Gardner equation
During calculation interface problem using DEtools [rifsimp]

The problem is that this function only works for integer exponents

Is there another way to overcome this problem

 


 

> 

``
> 

restart; with(PDEtools); declare(u(t, x), A(t), B(t), F(t))

` u`(t, x)*`will now be displayed as`*u

  

` A`(t)*`will now be displayed as`*A

  

` B`(t)*`will now be displayed as`*B

  

` F`(t)*`will now be displayed as`*F

 (1)
> 

det_eqs := [2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx)) = 0, 2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx)) = 0, 2*(diff(Lambda1(t, x, u, ux, uxx), uxx))*B(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*B(t)*uxx+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*F(t)*u+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n*ux = 0, 2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*ux+2*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*uxx-2*(diff(Lambda1(t, x, u, ux, uxx), ux))+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x)) = 0, 3*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*B(t)+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*B(t)*uxx+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*A(t)*u^n*ux = 0, ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))-ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))+uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))+2*uxx*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))+diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x) = 0, 2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*A(t)*u^n*ux+4*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*B(t)+4*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*B(t)*uxx+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*B(t)*uxx^2+4*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*B(t)+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*F(t)+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*B(t)*uxx+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*F(t)*u+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n*n*ux^2/u+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*A(t)*u^n*ux^2+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*B(t)*uxx+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*A(t)*u^n*ux = 0, 2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*B(t)*uxx+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*A(t)*u^n*ux^3+ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*B(t)*uxx+ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*A(t)*u^n*ux^2-(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*A(t)*u^n*ux^2-ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*F(t)*u-2*uxx*(diff(Lambda1(t, x, u, ux, uxx), ux))*A(t)*u^n-(diff(Lambda1(t, x, u, ux, uxx), x))*A(t)*u^n+uxx*(diff(Lambda1(t, x, u, ux, uxx), uxx))*F(t)+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*F(t)*u+2*ux^2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*F(t)+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*B(t)*uxx^2+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), x))*B(t)+ux^2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), u))*B(t)+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*F(t)+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*B(t)*uxx^3-ux*(diff(Lambda1(t, x, u, ux, uxx), ux))*F(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*B(t)*uxx^2-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))*F(t)*u+uxx*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*B(t)+2*uxx*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*F(t)+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*A(t)*u^n+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*F(t)*u+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*A(t)*u^n*n*ux^2/u+3*uxx*(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n*ux/u+3*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*A(t)*u^n*ux+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*A(t)*u^n*ux+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*A(t)*u^n*ux-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))*A(t)*u^n*ux+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*A(t)*u^n*ux^2+2*uxx*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*F(t)*u-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*F(t)*u-(diff(Lambda1(t, x, u, ux, uxx), t))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*B(t)*uxx^2+2*uxx^2*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*A(t)*u^n+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*F(t)*u+2*(diff(Lambda1(t, x, u, ux, uxx), u))*B(t)*uxx+(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*B(t)*uxx+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*B(t)*uxx+(diff(Lambda1(t, x, u, ux, uxx), u))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*A(t)*u^n*ux-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*A(t)*u^n*ux+Lambda1(t, x, u, ux, uxx)*F(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), x), x))*B(t)+uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*F(t)*u+2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*A(t)*u^n*n*ux^3/u+(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n^2*ux^3/u^2-(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n*ux^3/u^2+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*A(t)*u^n*n*ux^2/u-(diff(Lambda1(t, x, u, ux, uxx), ux))*A(t)*u^n*n*ux^2/u = 0, diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx) = 0, diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx) = 0]

[2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx)) = 0, 2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx)) = 0, 2*(diff(Lambda1(t, x, u, ux, uxx), uxx))*B(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*B(t)*uxx+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*F(t)*u+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n*ux = 0, 2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*ux+2*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*uxx-2*(diff(Lambda1(t, x, u, ux, uxx), ux))+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x)) = 0, 3*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*B(t)+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*B(t)*uxx+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*A(t)*u^n*ux = 0, ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))-ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))+uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))+2*uxx*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))+diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x) = 0, 2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*A(t)*u^n*ux+4*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*B(t)+4*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*B(t)*uxx+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*B(t)*uxx^2+4*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*B(t)+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*F(t)+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*B(t)*uxx+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*F(t)*u+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n*n*ux^2/u+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*A(t)*u^n*ux^2+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*B(t)*uxx+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*A(t)*u^n*ux = 0, (diff(Lambda1(t, x, u, ux, uxx), u))*F(t)*u-ux*(diff(Lambda1(t, x, u, ux, uxx), ux))*F(t)+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*A(t)*u^n*ux-(diff(Lambda1(t, x, u, ux, uxx), x))*A(t)*u^n+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), x))*B(t)+ux^2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), u))*B(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*B(t)*uxx^2+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*F(t)*u+2*(diff(Lambda1(t, x, u, ux, uxx), u))*B(t)*uxx-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*F(t)*u+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*F(t)+uxx*(diff(Lambda1(t, x, u, ux, uxx), uxx))*F(t)+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*A(t)*u^n*n*ux^2/u+3*uxx*(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n*ux/u-(diff(Lambda1(t, x, u, ux, uxx), t))+2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*A(t)*u^n*n*ux^3/u+(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n^2*ux^3/u^2-(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n*ux^3/u^2+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*A(t)*u^n*n*ux^2/u-(diff(Lambda1(t, x, u, ux, uxx), ux))*A(t)*u^n*n*ux^2/u+2*uxx^2*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*A(t)*u^n+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*F(t)*u+uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*F(t)*u+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*B(t)*uxx^2+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*B(t)*uxx+(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*B(t)*uxx+uxx*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*B(t)+2*uxx*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*F(t)+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*A(t)*u^n+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*B(t)*uxx^3+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*B(t)*uxx^2+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*A(t)*u^n*ux^2+2*uxx*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*F(t)*u+3*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*A(t)*u^n*ux+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*A(t)*u^n*ux+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*A(t)*u^n*ux-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))*A(t)*u^n*ux+2*ux^2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*F(t)-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))*F(t)*u-ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*F(t)*u-2*uxx*(diff(Lambda1(t, x, u, ux, uxx), ux))*A(t)*u^n+ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*A(t)*u^n*ux^2-(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*A(t)*u^n*ux^2+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*B(t)*uxx+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*A(t)*u^n*ux^3+ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*B(t)*uxx-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*A(t)*u^n*ux+Lambda1(t, x, u, ux, uxx)*F(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), x), x))*B(t) = 0, diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx) = 0, diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx) = 0]

 (2)
> 

CL_multipliers := [Lambda1(t, x, u, ux, uxx)]

[Lambda1(t, x, u, ux, uxx)]

 (3)
> 

simplified_eqs := DEtools[rifsimp](det_eqs, CL_multipliers, mindim = 1)

Error, (in DEtools/Rif/setup) simplification only implemented for integer exponents

  
> 

``
> 

``
> 

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