and the thermal conductivity $k$ have the estimations $$c_* \cong T^3, \quad k \cong T^3 \left(1 + T^4\right)^{-2}.$$

It is also shown in [@ros79] that the one-dimensional equation (\[hydrogen.eq1\]), $$\label{Burg:mult.eq14}
 u_t = u^2 u_{xx}\,,$$ is related to the linear heat equation by a non-point transformation (Eq. (5) in [@ros79]). A similar relation was found in [@blu-kum80] for another representation of Eq. (\[Burg:mult.eq14\]). The non-point transformation of Eq. (\[Burg:mult.eq14\]) to the linear heat equation $$\label{hydrogen.eq2}
 w_s =  w_{\xi \xi}$$ is written in [@ibr83] as the differential substitution $$\label{hydrogen.eq3}
 t = s, \quad x = w, \quad  u =  w_\xi.$$ It is also demonstrated in [@ibr83], Section 20, that Eq. (\[Burg:mult.eq14\]) is the unique equation with nontrivial Lie-Bäcklund symmetries among the equations of the form $$u_t = f(u) + h (u, u_x), \quad f'(u) \not= 0.$$ The connection between Eq. (\[Burg:mult.eq14\]) and the heat equation is treated in [@rog85] as a reciprocal transformation [@rog85]. It is shown in [@rog86] that this connection, together with its extensions, allows the analytic solution of certain moving boundary problems in nonlinear heat conduction.

Our Example \[Burg:mult.exa4\] from Section \[samul:1\] reveals one more remarkable property of Eq. (\[Burg:mult.eq14\]). Namely, taking $n = 2$ and $f(u) = u^2$ 