X-axis discontinuity for plot with two ordinate axes - not in pgfplots manual

Question

Despite multiple ordinates and axes discontinuities appearing adjacent in the pgfplots manual, achieving both in the same plot is proving difficult.

Specifically, I have the following pgfplots plot with two y-axes (see MWE below)

I would like to have an x-axis discontinuity that breaks the x-axis into 2 intervals: the first ranging from (-4,-3) and the second ranging from (0,4). I would like to retain the border to the graph in the style of the answer to this post, which has a discontinuity on the y-axis. I have tries updating it with no success and i'm not sure how to adapt the answer to a plot with double y-axes.

Any help is appreciated.

MWE

\documentclass[tikz]{standalone}
\usepackage{pgf,pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\pgfplotsset{set layers}
\begin{axis}[scale only axis,
xlabel={$x$},
ylabel={Ordinate 1},
axis y line*=left,

xmin=-4.0, xmax=4.0
]

\addplot[red] {x^2}; \label{plot_one}
\end{axis}
\begin{axis}[scale only axis,
ylabel={Ordinate 2},
xmin=-4.0, xmax=4.0, 
axis y line*=right,
axis x line=none,

]

\addlegendimage{/pgfplots/refstyle=plot_one}\addlegendentry{plot 1}
\addplot[blue] {x}; \label{plot_two}
\addplot[green] {3*x};  \label{plot_three}
\addlegendentry{plot 2}
\addlegendentry{plot 3} 
\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document} 
\begin{tikzpicture}
\pgfplotsset{set layers}
\begin{axis}[
title={A confusing and unnecessary plot},
scale only axis,
xlabel={$x$},
ylabel={Ordinate 1},
axis y line*=left,      
xmin=-4, xmax=2,
xticklabels={-4,-4,-3,0,1,2,3,4},
x axis line style= { draw=none}
]                   
\addplot[
  red, samples=101,
  unbounded coords=jump,
  x filter/.expression={x<-3? x: (x>0? x-2: nan)},
  ] {x^2}; \label{plot_one}
  \path[-] (rel axis cs:0,0)     coordinate(botstart)
          --(rel axis cs:0.2,0)coordinate(interruptbotA)
         (rel axis cs:0.3,0)  coordinate(interruptbotB)
         --(rel axis cs:1,0)   coordinate(botstop);
         \path[-] (rel axis cs:0,1)     coordinate(topstart)
         --(rel axis cs:0.7,1) coordinate(interrupttopA)
         (rel axis cs:0.87,1)  coordinate(interrupttopB)
         --(rel axis cs:1,1)   coordinate(topstop);
\end{axis}
\draw(botstart)-- (interruptbotA) decorate[decoration=zigzag]{--(interruptbotB)} -- (botstop);
\draw(topstart) -- (topstop);
\begin{axis}[scale only axis,
ylabel={Ordinate 2},
xmin=-4.0, xmax=2, 
axis y line*=right,
axis x line=none,   
]                       
\addlegendimage{/pgfplots/refstyle=plot_one}
\addlegendentry{plot 1}
\addplot[blue, samples=101,
  unbounded coords=jump,
  x filter/.expression={x<-3? x: (x>0? x-2: nan)},
  ] {x}; \label{plot_two}
\addplot[green, samples=101,
  unbounded coords=jump,
  x filter/.expression={x<-3? x: (x>0? x-2: nan)},
  ] {3*x};  \label{plot_three}
\addlegendentry{plot 2}
\addlegendentry{plot 3} 
\end{axis}
\end{tikzpicture}
\end{document}

Discontinuous axis taken from here: https://tex.stackexchange.com/a/386663/8650

Answer 2

This is as far as I got. I tried using axis x discontinuity but there is no way to place it into the right position. It wants to go to the right of 0, or to the left of xmax if negative.

I also ran into some bugs regarding the axis environment and shifting. If you put the axis into a scope and shift the scope, the only thing moved is the legend. If you shift the axis, the bounding box is not shifted.

\documentclass{standalone}
\usepackage{pgf,pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\pgfplotsset{set layers}% ???
\begin{axis}[scale only axis, width=1cm, height=4cm,
xlabel=\vphantom{$x$},
ylabel={Ordinate 1},
axis y line*=left,

xmin=-4.0, xmax=-3.0,
ymin=0.0, ymax=16.0,
xtick={-4,-3}
]

\addplot[red] {x^2}; \label{plot_one}
\coordinate (SE) at (rel axis cs: 1,0);
\coordinate (NE) at (rel axis cs: 1,1);
\end{axis}
\begin{axis}[scale only axis, width=1cm, height=4cm,
xmin=-4.0, xmax=-3.0, 
axis y line=none,
axis x line=none,
ymin=-12, ymax=12.0,
]

\addplot[blue] {x};
\addplot[green] {3x};
\end{axis}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{axis}[xshift=2cm,
scale only axis, width=4cm, height=4cm,
xlabel={$x$},
axis y line=none,

xmin=0.0, xmax=4.0,
ymin=0.0, ymax=16.0,
name=right
]

\addplot[red] {x^2}; \label{plot_one}
\coordinate (SW) at (rel axis cs: 0,0);
\coordinate (NW) at (rel axis cs: 0,1);
\end{axis}
\begin{axis}[xshift=2cm,
scale only axis, width=4cm, height=4cm,
ylabel={Ordinate 2},
xmin=0.0, xmax=4.0, 
axis y line=right,
axis x line=none,
ymin=-12, ymax=12.0,
]

\addlegendimage{/pgfplots/refstyle=plot_one}\addlegendentry{plot 1}
\addplot[blue] {x}; \label{plot_two}
\addplot[green] {3*x};  \label{plot_three}
\addlegendentry{plot 2}
\addlegendentry{plot 3} 
\end{axis}
\path (7cm,0);% kludge to fix bounding box
\draw[red] (SE) -- (SW);
\draw[red] (NE) -- (NW);
\end{tikzpicture}
\end{document}