my @equations = /\$([^$]+)\$/;
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To get all matches, you'd need the /g option.  Also, $] is a special variable, so the dollar sign must be escaped here.

Your regex won't work because of greediness. I think using /g as in page 210 of the cookbook might make a regex work.

LaTeX::Parser from your suggested search is in version 0.01 and buggy. That's the same package I meant above.

EDIT: Ah, you mean LaTeX::TOM! Perfect, I'll try that.

Greediness isn't an issue here, because the character class [^\$] doesn't allow a $ to be part of the captured fragments.

Alternatively, you could use a non-greedy pattern: /\$(.+?)\$/g

my $latex = q|We find that the generical scale behavior of structure f
+unctions in the inertial range is not self-similar $S_n(\ell)\propto 
+\ell^{\zeta_n}$ but includes an \u201cexponential self-similar\u201d 
+behavior $S_n(\ell) \propto \exp[\zeta_n\alpha^{-1} \ell^{\alpha}]$ w
+here $\alpha$ is a parameter proportional to the inverse of the logar
+ithm of the Reynolds number.|;

my @equations = $latex =~ /\$(.+?)\$/g;

say for @equations;
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Output:

S_n(\ell)\propto \ell^{\zeta_n}
S_n(\ell) \propto \exp[\zeta_n\alpha^{-1} \ell^{\alpha}]
\alpha
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Thank you, Eliya. That code is clear and now my problem is solved.