Recent content by fian

Alright, I see. Thank you for your explanation. I got something new through this discussion beside what I asked.

thank you, your hints help improve my understanding and insight. However, I do need to learn more. what i can conclude from the contribution of term uxxx to the dispersion relation is that the dispersion is nonlinear, resulting that there is change in velocities. I think, it means that the...

Thank you for replying, Simon. So, ## uu_x ## explain how the tension works to waves as they propagate, doesn't it? does tension relate to wave steepening? I read that the nonlinear term in KdV represent the nonlinear wave steepening (I forgot where I found it, but I wrote it in my note book...

Thank you for replying. It gives me some hints to study more. This is how i understand it. Let u be the elevetion of wave. u^2 represents the interaction of waves which causes energy transfer among the waves. Am I correct?

Here is a graph of y=sin(x) that may help you to understand more about relation sin(x)=sin(pi-x), 0 =< x <= pi/2. It shows some chosen values of x which are pi/6 and pi/4. Sin (5pi/6) = sin (pi - (pi/6)) = sin (pi/6) = 1/2

Thank you for correcting me, micromass

Ah, yes. Sorry. I used my daily speaking. You said right about the definition of line. I am correcting it. It should have been the length or magnitude of the line connecting the points. So the distance is the length of the line.

It's the case in Euclide geometry

If you have two points, any lines connecting them are the distance, but the shortest distance is the straight line connecting them.

Can anybody please help me to understand the physical interpretation of kdv eq.?

I suggest "Contemporary Abstract Algebra" by Joseph A. Gallian. I think it's quite easy to understand this book. I read this book when the first time I learned abstract algebra

Thank you :)

Sorry, It seems like i accidentally posted it twice, it is because of the low connection.

Here is one of the KdV form u_t + u_x + uu_x + u_{xxx} = 0 Where u is elevation, x is spatial variable, and t is time variable. The first two terms describe the linear water wave, the third term represent the nonlinear effect, and the last term is the dispersion. From what i understand, the...

Here is one of the KdV form u_t + u_x + uu_x + u_{xxx} = 0 Where u is elevation, x is spatial variable, and t is time variable. The first two terms describe the linear water wave, the third term represent the nonlinear effect, and the last term is the dispersion. From what i understand, the...