RE: "how to pass the equations from normal variables to dimensionless?"

I couldn't find the paper you are talking about, but I suspect the author used a the technique of "non-dimensionalisation" ... it consists of making appropriate change of variable to remove the dimension and simplify the equation https://en.wikipedia.org/wiki/Nondimensionalization

RE: "The second and most important doubt is how to use 4th range kutta of 2nd ODE to find a numerical solution to the problem in this context"

Either they used a solver already implemented in their programming software or they wrote the code themselves...You would have to discretise the equations and implement the code to solve the equation and then plot the graphs of the solution. 

https://en.wikipedia.org/wiki/Runge–Kutta_methods

Browse more information on the method on google, especially for higher dimensions.

I think you are looking for the solution outlined in the Maple language described below - see also the refs.

It should be straight forward to convert to Matlab or some other language.

Regards

http://www.maplesoft.com/applications/view.aspx?SID=131117&view=html

Santanu Kumar Patro here is the article . I want to obtain the graphics shown in the article by myself but i can't do it

Thanks Santanu . The article is interesting .  I'm a little bit short on diferential equations (i'll study it next year) , in terms of programming if you give me a code i think i can understand it . Many thanks again .