So the solution depend on the 3 parameters et and the length of
the interval .
The number of physical dimension is 2 ; there are a space dimension and a time one.
As a conclusion of this remarks, the solution depends on a unique parameter.
The different dimensions are :
In order to determine the parameter on which the solution depend, we have to find a no-dimensionnal number. This is equivalent to find , and which verify :
Another way to prouve that the solution of the KSE depends only on a no-dimensionnal parameter is to transform the dimensionnal equation to a no-dimensionnal one. We first have to dertermine the values of reference. There are different possibities, one of these is :
This result is very useful, the rest fo the study will be realized for , and . We only change the value of . That simplify the study and the writing of the code to simulate the KSE.