publications - Exact results found, but not reported

I am writing a physics paper, and I have decided not to write down explicit equations I have found since they are incredibly long. Instead I just report plots showing the behaviour resulting from these equations.

Is it deprecable to say something like the following?

We have found analytic results, but we do not report them here for sake of brevity.

Answer

Idealistically, a paper should aspire to contain all the information required for reproducing its empirical results and verifying its deductive results with reasonable effort. Just writing the suggested sentence, however, does not allow for this, as someone would have to redo your work on finding those equations from scratch.

This may drastically reduce the usefulness of your paper, as it unnecessarliy increases the amount of work other people have to put in using your results and decreases their perceived soundness (see Fermat’s Last Theorem for an extreme example). This may also be harmful from an egoistical point of view as it does not improve your popularity amongst others in your field and you may receive less citations.

Depending on how exactly your equations were derived and look like, the following ways to include or not include them may be appropriate:

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  From [equations derived in the paper] we can obtain closed solutions for [variables] using [standard technique or computer algebra system], which we use in the following.

  
  

  
  


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  From [equations derived in the paper], we obtain closed solutions for [variables] (see Appendix X).

  
  

  
  


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  If the target journal does not allow for appendices and has a content limit (in which case it will usually be a letter journal), the following may be acceptable:

  
  
  

  
  

  From [equations derived in the paper] we derived analytical results for [variables]. For brevity’s sake, these results are not given here and will be published elsewhere.

  
  

  
  

  Something similar may also be appropriate if you are publishing in a journal of another discipline, e.g., you are publishing in a medical journal as your equations are relevant for an imaging technique.

  
  

  Either way, it should go without saying that publishing the results elsewhere should be a realistic endeavour and actually be intended. Also, if you are not giving too much away, it would be better in terms of soundness and acceptance to actually publish your analytical work first.

  
  

As always, you will likely get a better answer from someone familiar with your work and field, such as your supervisor.