# Interaction tetween two waves soliton

1. Mar 30, 2013

### alejandrito29

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

how i find a equation for the interaction between the right and left waves $$\pm c$$

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

Last edited: Mar 30, 2013
2. Mar 30, 2013

### Simon Bridge

Hang on - let me tidy thatup for you...
$\newcommand{\sech}{\operatorname{sech}}$
Great - now, what sort of interaction did you have in mind?
For simple displacement - i.e. these are water waves - then the two waves would produce the superposition $y=A \sech^2 (k(x + ct))+A \sech^2 (k(x - ct))$. But I suspect these equations are for the envelope for the soliton.

Perhaps you are doing an exercize in nonlinear superposition?
http://kasmana.people.cofc.edu/SOLITONPICS/