## KdV Equation - Modelling Soliton

 Quote by Studiot $${c_0} = \sqrt {gh_0^2}$$ is the velocity of gravity waves.
Is is not:

$${c_0} = \sqrt {gh_0}$$??

 Sorry I'm absolutely struggling today. One with the equation format on the forum. and two just in general. So I now sub in eta into the KdV equation for water waves in order to solve for amplitude for a certain wave velocity, time and displacement?
 Yes you are right c0 = √gh0 Well spotted.
 No worries :) So where do I go from here? ha I mean I dont really see what I can do with the solution when I dont know any of the variables?
 Surely you have the real world variables in the last version of the equation I posted plus the sketch? If you want to consider the conditions under which a soliton will form then you need to go back to the KDV and consider varying each term. The third term is the nonlinear one which is added to include for dispersion.
 Sorry I was very new to the topic earlier and had no real idea. I have done some reading and I think I am progressing in terms of understanding. My main remaining question is this: Can I predict the amplitude of the solitons using the KdV equation? I mean the solution to the equation gives me the wave profile if I am not mistaken, that is assuming you know the variables required. In my case I have all the variables except the soliton amplitude (as I want to predict this) therefore the solution is of no help to me as I also do not have the wave profile. I hope my question makes sence, and once again Thanks Studiot!
 hi im going to start a small project on 'elementary solution of kdv equation'. can someone tell me to do this project what should i learn first. also tell me what are the necessary definitions that i should know.