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Nov 30, 2018 at 16:46 comment added MathDG Let us continue this discussion in chat.
Nov 30, 2018 at 15:41 comment added Willie Wong In that case, it may be worthwhile to include in your question some discussion of where this equation comes from and why you cannot do the nonlinear change of variables that I suggested, to get a more targeted response.
Nov 30, 2018 at 15:16 comment added MathDG @Willie Wong - thank you very much for the suggestion but unfortunately I can not transform it
Nov 30, 2018 at 15:07 history edited YCor CC BY-SA 4.0
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Nov 30, 2018 at 14:42 comment added Willie Wong Actually, can you not transform this into a standard eikonal equation? If you let $F:\mathbb{R}\to\mathbb{R}$ be a primitive of $(\alpha z^n + \beta)^{-\frac12}$, then your equation is equivalent to $|\nabla F(\omega)| = 1$ which is the standard eikonal equation.
Nov 30, 2018 at 14:36 comment added MathDG @Willie Wong - Thank you very much!
Nov 30, 2018 at 14:33 comment added Willie Wong It looks like an eikonal equation with a nonlinear wave speed; that's what I would search for anyway as a start.
Nov 30, 2018 at 13:47 comment added MathDG @Piotr Hajlasz - Yes, there was a mistake, thank you!
Nov 30, 2018 at 13:45 history edited MathDG CC BY-SA 4.0
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Nov 30, 2018 at 13:31 comment added Piotr Hajlasz I do not understand it. From the equation you get that $\omega=(-\beta/\alpha)^{1/n}$ is constant. There must be a mistake in your statement.
Nov 30, 2018 at 12:46 history undeleted MathDG
Nov 30, 2018 at 12:45 history deleted MathDG via Vote
Nov 30, 2018 at 12:37 history asked MathDG CC BY-SA 4.0