# Question:How do I find Lax pair for this equation?

## Question:How do I find Lax pair for this equation?

Maple 2018

Hello
In this example, we have the KdV equation
u[t] - 6 uu[x] + u[xxx] = 0
I would like to find the Lax pair for the KdV equation, which are
Lψ=λψ
ψ[t] = Mψ
where
L[t]+ML-LM = 0  called a compatibility condition
So, I will start from this purpose
Then we will assume M in the form
we will assume M in the form
M := a3*Dx^3+a2*Dx^2+a1*Dx+a0
then by using M and L in the form   L[t]+ML-LM = 0 we can find
( ) Dx^5+( ) Dx^4+( ) Dx^3+( ) Dx^2+( ) Dx+( )=0
then we can find a_i ;i=0,1,2,3
In the following maple code to do that
my question is
. ?How I can continue the solution to get a_i ;i=0,1,2,3 using maple code -
.?is thir any maple packge to find Lax pair for PDE -

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in this exampile we have KdV equation

I would like to find the Lax pair for the KdV equation, which are

Lψ=λψ

where

+ML-LM = 0    called  a compatibility  condition

So, I  will start from this purpose

L:=-Dx^2+u;

then we will assume M in the form

M := a3*Dx^3+a2*Dx^2+a1*Dx+a0

then by using M and L in the form +ML-LM = 0 we can find

( ) Dx^5+( ) Dx^4+( ) Dx^3+( ) Dx^2+( ) Dx+( )=0

then we can find a_i ;i=0,1,2,3

in the fllowing maple code to do that

my question is ;

1) How I can continue the solution  to get a_i ;i=0,1,2,3 using maple code  ?

2) is thir any maple packge to find  Lax pair for PDE ?

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