Automatically replace underscore with \textunderscore for PDF strings, e.g. with \pdfstringdefDisableCommands

Question

Is it possible to mimic the output of

\section{\texorpdfstring{$x_1$}{x\_1}}

using \section{$x_1$} and \pdfstringdefDisableCommands{...} ? I've only seen this answer, which tries to do something similar, but it doesn't work (as they acknowledge). I'm not too concerned about warnings; I just want x_1 to appear in the bookmarks for the PDF, while not having \texorpdfstring{...}{...} for every instance of an underline.

---

MWE for the error generated by tikz when using @StevenB.Segletes's first solution:

\documentclass{article}
\usepackage{hyperref}
%\usepackage{tikz} % OK
\let\svus_
\catcode`_=\active
\gdef_{\texorpdfstring{\svus}{\string_}}
%%%

% pgfmathparser.code.tex
% ! Missing \endcsname inserted.
% <to be read again> 
%                    \svus 
% l.251 ...mnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ}
% \usepackage{tikz}

%%%
\begin{document}
\tableofcontents
\section{$x_1$}
Document math, $a^3_1$ should be no problem
\section{$y_1$}
Does This_work?
\end{document}

Answer 1

Recall that hyperref warns you about the subscript character with something like

Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref)                removing `subscript' on input line 33.  

So clearly hyperref knows that it encounters a subscript character. All you need to do is to tell hyperref that, the next time you see _, instead of a warning, you put that character into the pdf toc.

The following code does that.

\documentclass{article}
\usepackage{tikz}
\usepackage{hyperref}
\makeatletter
\def\subscripttext{subscript}
\def\HyPsd@CatcodeWarning#1{%
  \def\argone{#1}
  \ifx\subscripttext\argone
    \expandafter\def\expandafter\HyPsd@String\expandafter{\HyPsd@String_}%
  \else
    \HyPsd@Warning{%
      Token not allowed in a PDF string (%
      \ifHy@unicode
        Unicode%
      \else
        PDFDocEncoding%
      \fi
      ):%
      \MessageBreak removing `\HyPsd@RemoveCmdPrefix#1'%
    }%
  \fi
}
\begin{document}
\tableofcontents
\section{$x_1$}
    Document math, $a^3_1$ should be no problem
\section{$y_1$}
    Does This_work?
\end{document}

This approach allows you to not setting the catcode of _. There are only this many special characters and a bunch of packages are competing with each other for a chance to define the activated characters. TikZ, as you noticed, is an expert in that sort.

Answer 2

You can make the underscore math active.

You'll get warnings

Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref)                removing `math shift' on input line 17.

but the output will be as expected.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{tikz} % OK
\usepackage{hyperref}
\usepackage{bookmark}
\AtBeginDocument{%
  \begingroup\lccode~=_ \lowercase{\endgroup\let~\sb}%
  \mathcode_="8000 \catcode_=12
}
\begin{document}
\tableofcontents
\section{$x_1$}
Document math, $a^3_1$ should be no problem
\section{$y_1$}
This_works and also_this.
\end{document}

Answer 3

Here I make _ active to accomplish it. Not sure if that works for your need.

\documentclass{article}
\usepackage{hyperref}
\let\svus_
\catcode`\_=\active
\gdef_{\texorpdfstring{\svus}{\string_}}
\begin{document}
\tableofcontents
\section{$x_1$}
Document math, $a^3_1$ should be no problem
\section{$y_1$}
Does This_work?
\end{document}

Perhaps a better way is to use \mathcode, so that _ is not active, but catcode-12 inside the document:

\documentclass{article}
\usepackage{hyperref}
\let\svus_
\mathcode\number`\_="8000
\begingroup\lccode`\~=`\_ \lowercase{\endgroup\def~}%
  {\texorpdfstring{\svus}{\string_}}
\catcode`\_=12
\begin{document}
\tableofcontents
\section{$x_1$}
Document math, $a^3_1$ should be no problem
\section{$y_1$}
Does This_work?
\end{document}