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Interaction tetween two waves soliton

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Hello if i have two waves soliton [tex]y=A \sech^2 (k(x \pm ct))[/tex], both solution of KdV differential equation

how i find a equation for the interaction between the right and left waves [tex] \pm c [/tex]

i think on supperposition waves, [tex]y=A \sech^2 (k(x + ct))+B \sech^2 (k(x - ct))[/tex], but i dont understand if the superposition represent to the interaction between both waves.

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