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unsure how to expand a LAX pair for KDV equation

0

$begingroup$

This is my first post so im not sure how to make it all mathsy so im going to write it on here, I know that to find the lax equation you find [LM-ML]=0 but im struggling to follow the expansion,

for eg $$L=left(fracddxright)^2+u$$
$$M=aleft(fracddxright)^3+bufracddx+cfracdudx$$

so LM would be $=a(d/dx)^5+$(on the book it says $b(d/dx)(u(d/dx)^2+(du/dx)(d/dx)$) i am unsure how this part comes about, ive tried to expand it and do it all but it doesn't simplify to that

im sorry if it doesnt look clear, again this is my first post.

classical-mechanics integrable-systems lax-pair

share|cite|improve this question

edited Mar 20 at 0:29

clathratus

5,0361438

asked Mar 19 at 21:58

123123123123

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  By "d/dx^2" do you mean $$left(fracddxright)^2$$ or $$fracddx^2$$ or anything else?
  $endgroup$
  – clathratus
  Mar 19 at 22:16
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  (d/dx)^2, sorry for not making that clear
  $endgroup$
  – 123123
  Mar 19 at 22:25
  

  
  
  
  

add a comment | 

0

$begingroup$

This is my first post so im not sure how to make it all mathsy so im going to write it on here, I know that to find the lax equation you find [LM-ML]=0 but im struggling to follow the expansion,

for eg $$L=left(fracddxright)^2+u$$
$$M=aleft(fracddxright)^3+bufracddx+cfracdudx$$

so LM would be $=a(d/dx)^5+$(on the book it says $b(d/dx)(u(d/dx)^2+(du/dx)(d/dx)$) i am unsure how this part comes about, ive tried to expand it and do it all but it doesn't simplify to that

im sorry if it doesnt look clear, again this is my first post.

classical-mechanics integrable-systems lax-pair

share|cite|improve this question

edited Mar 20 at 0:29

clathratus

5,0361438

asked Mar 19 at 21:58

123123123123

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  By "d/dx^2" do you mean $$left(fracddxright)^2$$ or $$fracddx^2$$ or anything else?
  $endgroup$
  – clathratus
  Mar 19 at 22:16
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  (d/dx)^2, sorry for not making that clear
  $endgroup$
  – 123123
  Mar 19 at 22:25
  

  
  
  
  

add a comment | 

$begingroup$

This is my first post so im not sure how to make it all mathsy so im going to write it on here, I know that to find the lax equation you find [LM-ML]=0 but im struggling to follow the expansion,

for eg $$L=left(fracddxright)^2+u$$
$$M=aleft(fracddxright)^3+bufracddx+cfracdudx$$

so LM would be $=a(d/dx)^5+$(on the book it says $b(d/dx)(u(d/dx)^2+(du/dx)(d/dx)$) i am unsure how this part comes about, ive tried to expand it and do it all but it doesn't simplify to that

im sorry if it doesnt look clear, again this is my first post.

classical-mechanics integrable-systems lax-pair

share|cite|improve this question

edited Mar 20 at 0:29

clathratus

5,0361438

asked Mar 19 at 21:58

123123123123

1

$endgroup$

share|cite|improve this question

edited Mar 20 at 0:29

clathratus

5,0361438

asked Mar 19 at 21:58

123123123123

1

share|cite|improve this question

edited Mar 20 at 0:29

clathratus

5,0361438

asked Mar 19 at 21:58

123123123123

1

edited Mar 20 at 0:29

clathratus

5,0361438

edited Mar 20 at 0:29

clathratus

5,0361438

asked Mar 19 at 21:58

123123123123

1

asked Mar 19 at 21:58

123123123123

1