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With a basic understanding of physical geometry we can understand this difference. A soliton is a KIND of pseudosphere created by the rotation of a tactrix, however, this particular kind of pseudosphere is harmonically generated by the negation of itself. We can say that if the natural growing pseudosphere has a one dimensional rotational property then the ...


I'm TAing a nonlinear waves course this quarter, so I'll bite on this question. Throughout this discussion, let's take the Korteweg de Vries (KdV) equation as our model system, that is $$\eta_t+\eta\eta_x +\eta_{xxx} = 0$$ where $\eta$ is the (non-dimensionalized) free surface displacement. This equation can be derived in a variety of ways, in ...

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