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A new algorithm for finding Hirota bilinear form (D-Operator) of NPDE?

Salim Mahmood, Soran university
Posted 8 months ago
POSTED BY: Salim Mahmood
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Thank you so much! I really appreciate that you mentioned each equation—this is incredibly helpful. However, the two equations you referred to are among the easier ones. In front of me, I have more than 20 equations, which I am finding difficult to handle. I hope to find a way to construct a well-organized and systematic approach to Hirota's method that can help me manage these equations effectively.
POSTED BY: Salim Mahmood
POSTED BY: Gianluca Gorni
POSTED BY: Salim Mahmood

Here is just a start:

Clear[u, x, t, \[CapitalPhi]];
eq21 = D[u[x, t], t] + 5 D[u[x, t] D[u[x, t], {x, 2}], x] + 
  5 u[x, t]^2 D[u[x, t], x] + D[u[x, t], {x, 5}]
eq22 = u -> Function[{x, t}, 6 D[Log[\[CapitalPhi][x, t]], {x, 2}]]
subst = (eq21 /. eq22)/6;
eq23 = Integrate[subst, x] // Together // Numerator
POSTED BY: Gianluca Gorni
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