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I am studying a one-component reaction–diffusion equation: $$ \partial_t u(x,t) = D \partial^2_x u(x,t) + R\left(u(x,t)\right)$$ Looking at systems that exhibit a peak solution (solitary localized structures) - are there known general conditions for peak splitting?

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    $\begingroup$ I don't see how this can be approached even without definition of $R$. $\endgroup$ – Gert Aug 13 '20 at 13:58
  • $\begingroup$ Yes, I wanted to know whether there are conditions for R such that there is this possibility. In general I am looking at reaction-diffusion equations where the R is a modified logistic growth term... $\endgroup$ – Ohm Aug 15 '20 at 11:31

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