I am solving the KdV equation using Hirota's method. I used the perturbation series to solve for the one-, two-, three-, and N-soliton solutions but I am having some challenges in the substitution of the D-operator in the series to solve for the unknown functions.
More faimath method to solve KdV eq is inverse scattering method. See, e.g. Gardner et al: Phys. Rev. Letters 19(1967)1095.
If you are interested in N-soliton solution of the KdV eq., see Novikov et al: "Soliton Theory: The inverse Scattering Method", Plenum, New York, 1984)
i have solved for the one soliton and two soliton using the hirotas method so I want to use induction on the N-soliton.
Why are you not interested in using inverse scattering method which is much easier than Hirota's method.
It is a bad project. The problem should be to solve the equation not the means.
How can I reduce two soliton solution to single soliton as t tends to + and - infinity. Also want to compute the phase shift the soliton undergoes as t varies from -infinity to +infinity
See http://www.math.upenn.edu/~jucurry/papers/soliton.pdf and references therein.
Thanks very much, have downloaded the paper. I will go through it and get back to you
N-soliton solution of of KdV eq. by Hirota's method is written there or reference therein
Yes I have seen it...thank you very much. Can I acknowledge you in my project?
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