Suppose that u(x, t) is the exact solutions of the nonlinear partial differential equations and xi=x+ct is the wave variable.
I expect that if you vary x and t between -5 and +5 the results will look sensible, and if you use values outside that it will give wrong results.
Try some values inside the area and some outside and see what happens. You may find that outside this you get zeros or infinities or the answer oscillates wildly with small changes of position. It may work close to the boundary, like (5,6) so you could try positions further away.
stable? isn't it about convergence of higher order perturbations, or other series components?
OK. Probably, everything should be in the book...The moment is the Energy by phase velocity, ρ=Wk/f, W is proportional to f, so it looks OK. ω=∂f/∂k, looks like ∂f/∂ρ ...oh, I can not imagine how it is described on the plot maybe like ∂f²/∂²ρ>0, which is a dispersion coefficient. It may have meaning for a forward wave. But what about backward wave? If you find an answer in the book, that will be interesting to see
This is research article and already published in SCI journal. Mention it your question and try it! Andrey Porokhnyuk
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