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
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.
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
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...