Transition to Asymptotic Coordinates

Let us transform (4.1.1) as follows. Let the leading terms of the asymptotic expansions of w for small and large t have the form 

Note that the original dependence (4.1.1), as well as the asymptotics (4.1.2) and (4.1.3) can be determined either theoretically or experimentally. 

By expressing the parameter r from the second equation in (4.1.4) and by substituting it into the first equation, we obtain 

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