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Question: Find all rational function solutions to the Kadomtsev-Petviashvili equation

Question:Find all rational function solutions to the Kadomtsev-Petviashvili equation

HBKodak 55 Maple
May 02 2022
1

Find all rational function solutions to the Kadomtsev-Petviashvili equation 
                         
(∂)/(∂x);

diff(u, t) + 6*u*diff(u, x) + diff(u, x, x, x) - diff(u, y, y) = 0;

by u = 2 
diff(ln, x, x)*f;

=(2 (((∂)^2)/(∂x^2) f) f-2 ((∂)/(∂x) f)^2)/(f^2);
 with 
f;
  =
(a[1 ]x+a[2] y+a[3] t+a[4])^2+(a[5] x+ a[6] y+a[7] t+a[8])^2+a[9], ;
where 
a[i], i=1..9, ;
are real constants.
 
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