I wish to obtain a solution to two coupled nanonlinear differential equations using perturbative expansion approach. In the expasanions, am interested in the eigenvectors (expansion coeeficients) and eigen values (Simple coeficients of V). In particular, I wish to plot the eigenvalues.
Am familiar with Mathematica and will like to write the algorithms and the plottings in it.
I have attached below a pdf file which describes the problem.
Thank you in advance.
Dear Musah,
I found the article to which your pdf refers and concluded that it would take me several hours to understand the problem. You can't be serious in your claim that your file 'describes the problem in detail'. You had to invest much more preparatory work and be much more explicit before you can count on help from volonteers, At least, this is the situation with me.
Thank you Professor Mutze for your point. I am sory for my exageration.
Trully, it took me several months to properly understand the relevant part of the paper. I have no problem with the theory (The part that concerned me, especially obtaing Equations (18) and (19)). I already obtained a similar solution (Equation (31)) but within Electrostatics formulation using the poisson-vorticity relation and continuity equations for the vorticity. This approach could only capture the zero order mode (Logarithmatic behaviour) of excitaion frequency (edge group velocity).
Right now, with some few lines in Mathematica, I can only get quite a large number of partial fractional sums which I failed to reduce to the Polygamma series sum (Eq. 30) in the paper.
I would like to write a code (in Mathematica or Matlab) that can reproduce the results in the papers using the Perturbative Expansion.
I noticed some missing terms in Equation (1) which I have included now in the attached pdf below.
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